## Lubotzky, Alexander

Compute Distance To:
 Author ID: lubotzky.alexander Published as: Lubotzky, Alexander; Lubotzky, A.; Lubotzky, Alex more...less External Links: MGP · Wikidata · GND · IdRef
 Documents Indexed: 159 Publications since 1979, including 5 Books 4 Contributions as Editor Co-Authors: 100 Co-Authors with 122 Joint Publications 2,527 Co-Co-Authors
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### Co-Authors

 40 single-authored 8 Kantor, William M. 7 Larsen, Michael Jeffrey 7 Magid, Andy Roy 7 Shalev, Aner 6 Bass, Hyman 6 Mozes, Shahar 5 Kassabov, Martin 5 Mann, Avinoam 5 Meiri, Chen 5 Samuels, Beth 5 Vishne, Uzi 5 Zimmer, Robert J. 4 Belolipetsky, Mikhail V. 4 Guralnick, Robert Michael 4 Jarden, Moshe 4 Pyber, László 3 Kaufman, Tali 3 Meshulam, Roy 3 Nikolov, Nikolay Valeriev 3 Phillips, Ralph Saul 3 Sarnak, Peter Clive 2 Becker, Oren 2 Ben-Ezra, David El-Chai 2 Capdeboscq, Inna 2 Evra, Shai 2 Gelander, Tsachik 2 Goldfeld, Dorian Morris 2 Grunewald, Fritz J. 2 Haran, Dan 2 Luria, Zur 2 Marion, Claude 2 Parzanchevski, Ori 2 Raghunathan, Madabusi Santanam 2 Reid, Alan W. 2 Rosenthal, Ron 2 Segal, Daniel 2 Thom, Andreas Berthold 2 Venkataramana, Tyakal Nanjundiah 1 Abért, Miklós 1 Aravinda, C. S. 1 Avni, Nir 1 Babai, László 1 Bekka, Mohammed el Bachir 1 Birman, Joan S. 1 Bleher, Frauke M. 1 Böge, Sigrid 1 Borovik, Alexandre V. 1 Breuillard, Emmanuel 1 Burger, Marc 1 Cappell, Sylvain E. 1 Chinburg, Ted 1 Conder, Marston D. E. 1 De Chiffre, Marcus 1 de Cornulier, Yves 1 du Sautoy, Marcus P. F. 1 Farb, Benson 1 Fisher, David Michael 1 Garion, Shelly 1 Glebsky, Lev Yu. 1 Goldman, William M. 1 Golubev, Konstantin 1 Gongopadhyay, Krishnendu 1 Grigorchuk, Rostislav Ivanovich 1 Guth, Lawrence David 1 Hrushovski, Ehud 1 Kazhdan, David A. 1 Kontorovich, Alex V. 1 Kowalski, Emmanuel 1 Kozma, Gady 1 Kropholler, Peter H. 1 Levit, Arie 1 Long, D. Darren 1 Long, Darren D. 1 Lubetzky, Eyal 1 Maher, Joseph 1 Malestein, Justin 1 Manning, Jason Fox 1 Margulis, Grigoriĭ Aleksandrovich 1 Martin, Benjamin M. S. 1 McCarthy, John D. 1 Minsky, Yair N. 1 Mj, Mahan 1 Myasnikov, Alexei G. 1 Nagnibeda, Tatiana V. 1 Oppenheim, Izhar 1 Pak, Igor 1 Rémy, Bertrand 1 Rogawski, Jonathan D. 1 Rosenzweig, Lior 1 Schillewaert, Jeroen 1 Shalom, Yehuda 1 Thilmany, François 1 van den Dries, Lou 1 Weaver, Anthony 1 Weigel, Thomas S. 1 Weinberger, Shmuel 1 Weiss, Benjamin 1 Wilson, John Stuart 1 Wilton, Henry John Rutley 1 Wu, Conan ...and 1 more Co-Authors
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### Serials

 16 Journal of Algebra 10 Israel Journal of Mathematics 5 Duke Mathematical Journal 5 Geometric and Functional Analysis. GAFA 5 Journal of the European Mathematical Society (JEMS) 5 Groups, Geometry, and Dynamics 4 American Journal of Mathematics 4 Bulletin of the London Mathematical Society 4 Geometriae Dedicata 4 Inventiones Mathematicae 4 Journal of the American Mathematical Society 4 Bulletin of the American Mathematical Society. New Series 4 Annals of Mathematics. Second Series 3 Mathematical Proceedings of the Cambridge Philosophical Society 3 Advances in Mathematics 3 European Journal of Combinatorics 3 Notices of the American Mathematical Society 3 Journal of Group Theory 3 Progress in Mathematics 2 Communications on Pure and Applied Mathematics 2 Acta Mathematica 2 Commentarii Mathematici Helvetici 2 Proceedings of the American Mathematical Society 2 Proceedings of the London Mathematical Society. Third Series 2 Transactions of the American Mathematical Society 2 International Journal of Algebra and Computation 2 Proceedings of the National Academy of Sciences of the United States of America 2 Transformation Groups 1 Journal d’Analyse Mathématique 1 Journal of Mathematical Physics 1 Archiv der Mathematik 1 Glasgow Mathematical Journal 1 Illinois Journal of Mathematics 1 Publications Mathématiques 1 Journal of Combinatorial Theory. Series B 1 Journal of Functional Analysis 1 Journal of the London Mathematical Society. Second Series 1 Journal of Pure and Applied Algebra 1 Journal für die Reine und Angewandte Mathematik 1 Memoirs of the American Mathematical Society 1 Publicationes Mathematicae Debrecen 1 The Quarterly Journal of Mathematics. Oxford Second Series 1 Topology 1 Ergodic Theory and Dynamical Systems 1 Combinatorica 1 Discrete & Computational Geometry 1 SIAM Journal on Discrete Mathematics 1 IMRN. International Mathematics Research Notices 1 L’Enseignement Mathématique. 2e Série 1 Comptes Rendus de l’Académie des Sciences. Série I 1 Pure and Applied Mathematics Quarterly 1 Contemporary Mathematics 1 Proceedings of the Steklov Institute of Mathematics 1 Algebra & Number Theory 1 Journal of Topology 1 Japanese Journal of Mathematics. 3rd Series 1 Bulletin of Mathematical Sciences 1 Forum of Mathematics, Sigma 1 Philosophical Transactions of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences 1 Modern Birkhäuser Classics
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### Fields

 117 Group theory and generalizations (20-XX) 48 Topological groups, Lie groups (22-XX) 35 Combinatorics (05-XX) 30 Number theory (11-XX) 14 Manifolds and cell complexes (57-XX) 7 Algebraic geometry (14-XX) 6 Abstract harmonic analysis (43-XX) 5 Field theory and polynomials (12-XX) 5 Functions of a complex variable (30-XX) 5 Dynamical systems and ergodic theory (37-XX) 5 Probability theory and stochastic processes (60-XX) 4 General and overarching topics; collections (00-XX) 4 Geometry (51-XX) 4 Computer science (68-XX) 3 Algebraic topology (55-XX) 3 Global analysis, analysis on manifolds (58-XX) 3 Information and communication theory, circuits (94-XX) 2 History and biography (01-XX) 2 Mathematical logic and foundations (03-XX) 2 Commutative algebra (13-XX) 2 Linear and multilinear algebra; matrix theory (15-XX) 2 $$K$$-theory (19-XX) 2 Several complex variables and analytic spaces (32-XX) 2 Functional analysis (46-XX) 2 Quantum theory (81-XX) 1 Order, lattices, ordered algebraic structures (06-XX) 1 Nonassociative rings and algebras (17-XX) 1 Measure and integration (28-XX) 1 Operator theory (47-XX) 1 Differential geometry (53-XX)

### Citations contained in zbMATH Open

148 Publications have been cited 3,089 times in 2,111 Documents Cited by Year
Ramanujan graphs. Zbl 0661.05035
Lubotzky, A.; Phillips, R.; Sarnak, P.
1988
Discrete groups, expanding graphs and invariant measures. Appendix by Jonathan D. Rogawski. Zbl 0826.22012
Lubotzky, Alexander
1994
Varieties of representations of finitely generated groups. Zbl 0598.14042
Lubotzky, Alexander; Magid, Andy R.
1985
Powerful $$p$$-groups. I: Finite groups. Zbl 0626.20010
Lubotzky, Alexander; Mann, Avinoam
1987
Subgroup growth. Zbl 1071.20033
Lubotzky, Alexander; Segal, Dan
2003
The probability of generating a finite classical group. Zbl 0718.20011
Kantor, William M.; Lubotzky, Alexander
1990
Abelian and solvable subgroups of the mapping class group. Zbl 0551.57004
Birman, Joan S.; Lubotzky, Alex; McCarthy, John
1983
Expander graphs in pure and applied mathematics. Zbl 1232.05194
Lubotzky, Alexander
2012
Discrete groups, expanding graphs and invariant measures. With an appendix by Jonathan D. Rogawski. Reprint of the 1994 original. Zbl 1183.22001
Lubotzky, Alexander
2010
The word and Riemannian metrics on lattices of semisimple groups. Zbl 0988.22007
Lubotzky, Alexander; Mozes, Shahar; Raghunathan, M. S.
2000
Hecke operators and distributing points on the sphere. I. Zbl 0619.10052
Lubotzky, A.; Phillips, R.; Sarnak, P.
1986
Subgroup growth and congruence subgroups. Zbl 0848.20036
Lubotzky, Alexander
1995
Hecke operators and distributing points on $$S^2$$. II. Zbl 0648.10034
Lubotzky, A.; Phillips, R.; Sarnak, P.
1987
Groups and expanders. Zbl 0787.05049
Lubotzky, A.; Weiss, B.
1993
Powerful $$p$$-groups. II: $$p$$-adic analytic groups. Zbl 0626.20022
Lubotzky, Alexander; Mann, Avinoam
1987
Ramanujan complexes of type $$\widetilde A_d$$. Zbl 1087.05036
Lubotzky, Alexander; Samuels, Beth; Vishne, Uzi
2005
Cayley graphs: Eigenvalues, expanders and random walks. Zbl 0835.05033
Lubotzky, Alexander
1995
Lattices in rank one Lie groups over local fields. Zbl 0786.22017
Lubotzky, Alexander
1991
Tree lattices. With appendices by H. Bass, L. Carbone, A. Lubotzky, G. Rosenberg, and J. Tits. Zbl 1053.20026
Bass, Hyman; Lubotzky, Alexander
2001
Group presentation, p-adic analytic groups and lattices in $$SL_ 2({\mathbb{C}})$$. Zbl 0541.20020
Lubotzky, Alexander
1983
Finitely generated groups of polynomial subgroup growth. Zbl 0811.20027
Lubotzky, Alexander; Mann, Avinoam; Segal, Dan
1993
Explicit constructions of Ramanujan complexes of type $$\widetilde A_d$$. Zbl 1135.05038
Lubotzky, Alexander; Samuels, Beth; Vishne, Uzi
2005
Combinatorial group theory for pro-p groups. Zbl 0489.20024
Lubotzky, Alexander
1982
Rank-1 phenomena for mapping class groups. Zbl 1025.20023
Farb, Benson; Lubotzky, Alexander; Minsky, Yair
2001
Representation growth of linear groups. Zbl 1142.22006
Larsen, Michael; Lubotzky, Alexander
2008
Small-diameter Cayley graphs for finite simple groups. Zbl 0702.05042
Babai, L.; Kantor, W. M.; Lubotzky, A.
1989
Free quotients and the first Betti number of some hyperbolic manifolds. Zbl 0876.22015
Lubotzky, Alexander
1996
Normal automorphisms of free groups. Zbl 0432.20025
Lubotzky, Alexander
1980
Subgroups of free profinite groups and large subfields of Q. Zbl 0485.20021
Lubotzky, Alexander; van den Dries, Lou
1981
On groups of polynomial subgroup growth. Zbl 0743.20040
Lubotzky, Alexander; Mann, Avinoam
1991
On some $$\Lambda$$-analytic pro-$$p$$ groups. Zbl 0819.20030
Lubotzky, Alexander; Shalev, Aner
1994
Counting hyperbolic manifolds. Zbl 1029.57021
Burger, M.; Gelander, T.; Lubotzky, A.; Mozes, S.
2002
Linear representations of the automorphism group of a free group. Zbl 1175.20028
Grunewald, Fritz; Lubotzky, Alexander
2009
Finite simple groups as expanders. Zbl 1161.20010
Kassabov, Martin; Lubotzky, Alexander; Nikolov, Nikolay
2006
The product replacement algorithm and Kazhdan’s property (T). Zbl 0980.20078
Lubotzky, Alexander; Pak, Igor
2001
Ramanujan complexes and high dimensional expanders. Zbl 1302.05095
Lubotzky, Alexander
2014
Invariable generation and the Chebotarev invariant of a finite group. Zbl 1248.20036
Kantor, W. M.; Lubotzky, A.; Shalev, A.
2011
A group theoretic characterization of linear groups. Zbl 0647.20045
Lubotzky, Alexander
1988
Presentations of finite simple groups: a quantitative approach. Zbl 1223.20024
Guralnick, R. M.; Kantor, W. M.; Kassabov, M.; Lubotzky, A.
2008
Presentations of finite simple groups: profinite and cohomological approaches. Zbl 1135.20024
Guralnick, Robert; Kantor, William M.; Kassabov, Martin; Lubotzky, Alexander
2007
Residually finite groups of finite rank. Zbl 0696.20031
Lubotzky, Alexander; Mann, Avinoam
1989
Free quotients and the congruence kernel of $$SL_ 2$$. Zbl 0495.20021
Lubotzky, Alexander
1982
Eigenvalues of the Laplacian, the first Betti number and the congruence subgroup problem. Zbl 0885.11037
Lubotzky, Alexander
1996
Pro-finite presentations. Zbl 0985.20017
Lubotzky, Alexander
2001
Polynomial representation growth and the congruence subgroup problem. Zbl 1134.20056
Lubotzky, Alexander; Martin, Benjamin
2004
Counting arithmetic lattices and surfaces. Zbl 1214.22002
Belolipetsky, Mikhail; Gelander, Tsachik; Lubotzky, Alexander; Shalev, Aner
2010
Variants of Kazhdan’s property for subgroups of semisimple groups. Zbl 0706.22010
Lubotzky, Alexander; Zimmer, Robert J.
1989
Finite groups and hyperbolic manifolds. Zbl 1113.57007
Belolipetsky, Mikhail; Lubotzky, Alexander
2005
Finite representations in the unitary dual and Ramanujan groups. Zbl 1080.22006
Lubotzky, Alexander; Shalom, Yehuda
2004
Automorphisms of groups and of schemes of finite type. Zbl 0517.14015
Bass, Hyman; Lubotzky, Alexander
1983
Counting finite index subgroups. Zbl 0862.20020
Lubotzky, Alexander
1995
Cohomology of unipotent and prounipotent groups. Zbl 0473.20031
Lubotzky, Alexander; Magid, Andy R.
1982
Cyclic subgroups of exponential growth and metrics on discrete groups. Zbl 0786.22016
Lubotzky, Alexander; Mozes, Shahar; Raghunathan, M. S.
1993
Linear-central filtrations on groups. Zbl 0817.20038
Bass, Hyman; Lubotzky, Alexander
1994
The proalgebraic completion of rigid groups. Zbl 1059.20036
Bass, Hyman; Lubotzky, Alexander; Magid, Andy R.; Mozes, Shahar
2002
Arithmetic quotients of the mapping class group. Zbl 1334.57017
Grunewald, Fritz; Larsen, Michael; Lubotzky, Alexander; Malestein, Justin
2015
The expected number of random elements to generate a finite group. Zbl 1042.20047
Lubotzky, Alexander
2002
Isoperimetric inequalities for Ramanujan complexes and topological expanders. Zbl 1339.05075
Kaufman, Tali; Kazhdan, David; Lubotzky, Alexander
2016
Invariable generation of infinite groups. Zbl 1318.20032
Kantor, William M.; Lubotzky, Alexander; Shalev, Aner
2015
Nonarithmetic superrigid groups: Counterexamples to Platonov’s conjecture. Zbl 0963.22005
Bass, Hyman; Lubotzky, Alexander
2000
Superrigidity for the commensurability group of tree lattices. Zbl 0839.22011
Lubotzky, A.; Mozes, S.; Zimmer, R. J.
1994
Dynamics and $$\operatorname{Aut}(F_N)$$ actions on group presentations and representations. Zbl 1266.20045
Lubotzky, Alexander
2011
Mixing properties and the chromatic number of Ramanujan complexes. Zbl 1328.05208
Evra, Shai; Golubev, Konstantin; Lubotzky, Alexander
2015
Stability and invariant random subgroups. Zbl 07145001
Becker, Oren; Lubotzky, Alexander; Thom, Andreas
2019
Subgroup growth of lattices in semisimple Lie groups. Zbl 1145.22004
Lubotzky, Alexander; Nikolov, Nikolay
2004
Presentations of finite simple groups: a computational approach. Zbl 1256.20008
Guralnick, R. M.; Kantor, W. M.; Kassabov, M.; Lubotzky, A.
2011
Beauville surfaces and finite simple groups. Zbl 1255.20008
Garion, Shelly; Larsen, Michael; Lubotzky, Alexander
2012
Lattices of minimal covolume in $$\mathrm{SL}_ 2$$: a nonarchimedean analogue of Siegel’s theorem $$\mu\geq \pi /21$$. Zbl 0731.22009
Lubotzky, Alexander
1990
Images of word maps in finite simple groups. Zbl 1318.20014
Lubotzky, Alexander
2014
Trees and discrete subgroups of Lie groups over local fields. Zbl 0676.22007
Lubotzky, Alexander
1989
Stability, cohomology vanishing, and nonapproximable groups. Zbl 1456.22002
De Chiffre, Marcus; Glebsky, Lev; Lubotzky, Alexander; Thom, Andreas
2020
Expansion of building-like complexes. Zbl 1405.55019
Lubotzky, Alexander; Meshulam, Roy; Mozes, Shahar
2016
Lattices of minimal covolume in $$\text{SL}_2$$ over local fields. Zbl 1026.22013
Lubotzky, A.; Weigel, Th.
1999
Not every uniform tree covers Ramanujan graphs. Zbl 1024.05021
Lubotzky, Alexander; Nagnibeda, Tatiana
1998
Enumerating boundedly generated finite groups. Zbl 1052.20017
Lubotzky, Alexander
2001
Functional equations and uniformity for local zeta functions of nilpotent groups. Zbl 0864.20020
Du Sautoy, Marcus P. F.; Lubotzky, Alexander
1996
Counting congruence subgroups. Zbl 1159.20329
Goldfeld, Dorian; Lubotzky, Alexander; Pyber, László
2004
On finite index subgroups of linear groups. Zbl 0597.20043
Lubotzky, Alexander
1987
Sieve methods in group theory. I: Powers in linear groups. Zbl 1283.20075
Lubotzky, Alexander; Meiri, Chen
2012
Division algebras and noncommensurable isospectral manifolds. Zbl 1123.58020
Lubotzky, Alexander; Samuels, Beth; Vishne, Uzi
2006
Quantum error correcting codes and 4-dimensional arithmetic hyperbolic manifolds. Zbl 1298.81052
Guth, Larry; Lubotzky, Alexander
2014
Embedding covers and the theory of Frobenius fields. Zbl 0502.20013
Haran, Dan; Lubotzky, Alexander
1982
High dimensional expanders. Zbl 1448.05125
Lubotzky, Alexander
2018
Powers in finitely generated groups. Zbl 0871.20038
Hrushovski, E.; Kropholler, P. H.; Lubotzky, A.; Shalev, A.
1996
Heegaard genus and property $${\tau}$$ for hyperbolic 3-manifolds. Zbl 1158.57018
Long, D. D.; Lubotzky, A.; Reid, A. W.
2008
A Moore bound for simplicial complexes. Zbl 1180.13028
Lubotzky, Alexander; Meshulam, Roy
2007
Random Latin squares and 2-dimensional expanders. Zbl 1306.05020
Lubotzky, Alexander; Meshulam, Roy
2015
Free prounipotent groups. Zbl 0503.20008
Lubotzky, Alexander; Magid, Andy R.
1983
Deformation theory and finite simple quotients of triangle groups. I. Zbl 1312.20030
Larsen, Michael; Lubotzky, Alexander; Marion, Claude
2014
Subgroup growth. Zbl 0857.20013
Lubotzky, Alexander
1995
Discrete groups of slow subgroup growth. Zbl 0877.20019
Lubotzky, Alexander; Pyber, László; Shalev, Aner
1996
Bounded generation and linear groups. Zbl 1059.20048
Abért, Miklós; Lubotzky, Alexander; Pyber, László
2003
Maximal abelian subgroups of free profinite groups. Zbl 0562.20013
Haran, Dan; Lubotzky, Alexander
1985
Cohomology, Poincaré series, and group algebras of unipotent groups. Zbl 0565.20023
Lubotzky, Alexander; Magid, Andy R.
1985
Finite simple groups of Lie type as expanders. Zbl 1257.20016
Lubotzky, Alexander
2011
Random normal subgroups of free profinite groups. Zbl 0928.20027
Jarden, Moshe; Lubotzky, Alexander
1999
Counting primes, groups, and manifolds. Zbl 1139.11324
Goldfeld, Dorian; Lubotzky, Alexander; Nikolov, Nikolay; Pyber, László
2004
Manifolds counting and class field towers. Zbl 1241.22014
Belolipetsky, Mikhail; Lubotzky, Alexander
2012
Torsion in profinite completions of torsion-free groups. Zbl 0829.20043
Lubotzky, Alexander
1993
Rigidity of group actions on locally finite trees. Zbl 0808.20031
Bass, Hyman; Lubotzky, Alexander
1994
Stability, cohomology vanishing, and nonapproximable groups. Zbl 1456.22002
De Chiffre, Marcus; Glebsky, Lev; Lubotzky, Alexander; Thom, Andreas
2020
Group stability and property (T). Zbl 07127791
Becker, Oren; Lubotzky, Alexander
2020
Random walks on Ramanujan complexes and digraphs. Zbl 1454.05114
Lubetzky, E.; Lubotzky, A.; Parzanchevski, O.
2020
From Ramanujan graphs to Ramanujan complexes. Zbl 1462.05235
Lubotzky, Alexander; Parzanchevski, Ori
2020
Stability and invariant random subgroups. Zbl 07145001
Becker, Oren; Lubotzky, Alexander; Thom, Andreas
2019
First order rigidity of non-uniform higher rank arithmetic groups. Zbl 1454.20001
Avni, Nir; Lubotzky, Alexander; Meiri, Chen
2019
Generalized triangle groups, expanders, and a problem of Agol and Wise. Zbl 1468.20083
Lubotzky, Alexander; Manning, Jason Fox; Wilton, Henry
2019
What is $$\dots$$ a thin group? Zbl 1423.20060
Kontorovich, Alex; Long, D. Darren; Lubotzky, Alexander; Reid, Alan W.
2019
The congruence topology, Grothendieck duality and thin groups. Zbl 1448.11080
Lubotzky, Alexander; Venkataramana, Tyakal Nanjundiah
2019
Random Steiner systems and bounded degree coboundary expanders of every dimension. Zbl 1426.05183
Lubotzky, Alexander; Luria, Zur; Rosenthal, Ron
2019
High dimensional expanders. Zbl 1448.05125
Lubotzky, Alexander
2018
The congruence subgroup problem for low rank free and free metabelian groups. Zbl 1386.20027
Ben-Ezra, David El-Chai; Lubotzky, Alexander
2018
Good cyclic codes and the uncertainty principle. Zbl 1436.94116
Evra, Shai; Kowalski, Emmanuel; Lubotzky, Alexander
2017
Isoperimetric inequalities for Ramanujan complexes and topological expanders. Zbl 1339.05075
Kaufman, Tali; Kazhdan, David; Lubotzky, Alexander
2016
Expansion of building-like complexes. Zbl 1405.55019
Lubotzky, Alexander; Meshulam, Roy; Mozes, Shahar
2016
Random methods in 3-manifold theory. Zbl 1354.57026
Lubotzky, Alexander; Maher, Joseph; Wu, Conan
2016
Presentations: from Kac-Moody groups to profinite and back. Zbl 1472.20117
Capdeboscq, I.; Lubotzky, A.; Rémy, B.
2016
Arithmetic quotients of the mapping class group. Zbl 1334.57017
Grunewald, Fritz; Larsen, Michael; Lubotzky, Alexander; Malestein, Justin
2015
Invariable generation of infinite groups. Zbl 1318.20032
Kantor, William M.; Lubotzky, Alexander; Shalev, Aner
2015
Mixing properties and the chromatic number of Ramanujan complexes. Zbl 1328.05208
Evra, Shai; Golubev, Konstantin; Lubotzky, Alexander
2015
Random Latin squares and 2-dimensional expanders. Zbl 1306.05020
Lubotzky, Alexander; Meshulam, Roy
2015
Geometry, groups and dynamics. ICTS program: groups, geometry and dynamics, Almora, India, December 3–16, 2012. Zbl 1318.30003
2015
Ramanujan complexes and high dimensional expanders. Zbl 1302.05095
Lubotzky, Alexander
2014
Images of word maps in finite simple groups. Zbl 1318.20014
Lubotzky, Alexander
2014
Quantum error correcting codes and 4-dimensional arithmetic hyperbolic manifolds. Zbl 1298.81052
Guth, Larry; Lubotzky, Alexander
2014
Deformation theory and finite simple quotients of triangle groups. I. Zbl 1312.20030
Larsen, Michael; Lubotzky, Alexander; Marion, Claude
2014
High dimensional expanders and property testing. Zbl 1365.68462
Kaufman, Tali; Lubotzky, Alexander
2014
Deformation theory and finite simple quotients of triangle groups. II. Zbl 1312.20031
Larsen, Michael; Lubotzky, Alexander; Marion, Claude
2014
The Galois group of random elements of linear groups. Zbl 1304.11125
Lubotzky, Alexander; Rosenzweig, Lior
2014
Finiteness properties and profinite completions. Zbl 1295.20029
Lubotzky, Alexander
2014
On conjugacy growth of linear groups. Zbl 1278.20064
Breuillard, Emmanuel; Cornulier, Yves; Lubotzky, Alexander; Meiri, Chen
2013
Representation varieties of Fuchsian groups. Zbl 1272.20054
Larsen, Michael; Lubotzky, Alexander
2013
Expander graphs in pure and applied mathematics. Zbl 1232.05194
Lubotzky, Alexander
2012
Beauville surfaces and finite simple groups. Zbl 1255.20008
Garion, Shelly; Larsen, Michael; Lubotzky, Alexander
2012
Sieve methods in group theory. I: Powers in linear groups. Zbl 1283.20075
Lubotzky, Alexander; Meiri, Chen
2012
Manifolds counting and class field towers. Zbl 1241.22014
Belolipetsky, Mikhail; Lubotzky, Alexander
2012
Sieve methods in group theory. II: The mapping class group. Zbl 1284.57017
Lubotzky, Alexander; Meiri, Chen
2012
Edge transitive Ramanujan graphs and symmetric LDPC good codes. Zbl 1286.94102
Kaufman, Tali; Lubotzky, Alexander
2012
Sieve methods in group theory. III: $$\operatorname{Aut}(F_n)$$. Zbl 1284.20035
Lubotzky, Alexander; Meiri, Chen
2012
Invariable generation and the Chebotarev invariant of a finite group. Zbl 1248.20036
Kantor, W. M.; Lubotzky, A.; Shalev, A.
2011
Dynamics and $$\operatorname{Aut}(F_N)$$ actions on group presentations and representations. Zbl 1266.20045
Lubotzky, Alexander
2011
Presentations of finite simple groups: a computational approach. Zbl 1256.20008
Guralnick, R. M.; Kantor, W. M.; Kassabov, M.; Lubotzky, A.
2011
Finite simple groups of Lie type as expanders. Zbl 1257.20016
Lubotzky, Alexander
2011
Lattices with and lattices without spectral gap. Zbl 1239.22003
Bekka, Bachir; Lubotzky, Alexander
2011
Remarks on proficient groups. Zbl 1239.20037
Guralnick, R. M.; Kantor, W. M.; Kassabov, M.; Lubotzky, A.
2011
Discrete groups, expanding graphs and invariant measures. With an appendix by Jonathan D. Rogawski. Reprint of the 1994 original. Zbl 1183.22001
Lubotzky, Alexander
2010
Counting arithmetic lattices and surfaces. Zbl 1214.22002
Belolipetsky, Mikhail; Gelander, Tsachik; Lubotzky, Alexander; Shalev, Aner
2010
Linear representations of the automorphism group of a free group. Zbl 1175.20028
Grunewald, Fritz; Lubotzky, Alexander
2009
On non-uniform Ramanujan complexes. Zbl 1279.11053
Samuels, Beth
2009
Representation growth of linear groups. Zbl 1142.22006
Larsen, Michael; Lubotzky, Alexander
2008
Presentations of finite simple groups: a quantitative approach. Zbl 1223.20024
Guralnick, R. M.; Kantor, W. M.; Kassabov, M.; Lubotzky, A.
2008
Heegaard genus and property $${\tau}$$ for hyperbolic 3-manifolds. Zbl 1158.57018
Long, D. D.; Lubotzky, A.; Reid, A. W.
2008
Elementary equivalence of profinite groups. Zbl 1200.20023
Jarden, Moshe; Lubotzky, Alexander
2008
Dimension expanders. Zbl 1154.15002
Lubotzky, Alexander; Zelmanov, Efim
2008
Presentations of finite simple groups: profinite and cohomological approaches. Zbl 1135.20024
Guralnick, Robert; Kantor, William M.; Kassabov, Martin; Lubotzky, Alexander
2007
A Moore bound for simplicial complexes. Zbl 1180.13028
Lubotzky, Alexander; Meshulam, Roy
2007
Finite simple groups as expanders. Zbl 1161.20010
Kassabov, Martin; Lubotzky, Alexander; Nikolov, Nikolay
2006
Division algebras and noncommensurable isospectral manifolds. Zbl 1123.58020
Lubotzky, Alexander; Samuels, Beth; Vishne, Uzi
2006
Isospectral Cayley graphs of some finite simple groups. Zbl 1110.05044
Lubotzky, Alexander; Samuels, Beth; Vishne, Uzi
2006
On presentations and second cohomology of some finite simple groups. Zbl 1123.20030
Korchagina, Inna; Lubotzky, Alexander
2006
Ramanujan complexes of type $$\widetilde A_d$$. Zbl 1087.05036
Lubotzky, Alexander; Samuels, Beth; Vishne, Uzi
2005
Explicit constructions of Ramanujan complexes of type $$\widetilde A_d$$. Zbl 1135.05038
Lubotzky, Alexander; Samuels, Beth; Vishne, Uzi
2005
Finite groups and hyperbolic manifolds. Zbl 1113.57007
Belolipetsky, Mikhail; Lubotzky, Alexander
2005
Finite representations of adelic groups, the congruence kernel and cohomology of finite simple groups. Zbl 1188.20046
Lubotzky, Alexander
2005
What is …property $$(\tau)$$? Zbl 1101.22300
Lubotzky, Alex
2005
The finitary Andrews-Curtis conjecture. Zbl 1114.20011
Borovik, Alexandre V.; Lubotzky, Alexander; Myasnikov, Alexei G.
2005
Some more non-arithmetic rigid groups. Zbl 1084.22007
Lubotzky, Alexander
2005
Polynomial representation growth and the congruence subgroup problem. Zbl 1134.20056
Lubotzky, Alexander; Martin, Benjamin
2004
Finite representations in the unitary dual and Ramanujan groups. Zbl 1080.22006
Lubotzky, Alexander; Shalom, Yehuda
2004
Subgroup growth of lattices in semisimple Lie groups. Zbl 1145.22004
Lubotzky, Alexander; Nikolov, Nikolay
2004
Counting congruence subgroups. Zbl 1159.20329
Goldfeld, Dorian; Lubotzky, Alexander; Pyber, László
2004
Counting primes, groups, and manifolds. Zbl 1139.11324
Goldfeld, Dorian; Lubotzky, Alexander; Nikolov, Nikolay; Pyber, László
2004
Normal subgroup growth of linear groups: the $$(G_2,F_4,E_8)$$-theorem. Zbl 1161.20305
Larsen, Michael; Lubotzky, Alexander
2004
The mathematics of Boris Weisfeiler. Zbl 1159.01340
Lubotzky, Alexander
2004
Subgroup growth. Zbl 1071.20033
Lubotzky, Alexander; Segal, Dan
2003
Bounded generation and linear groups. Zbl 1059.20048
Abért, Miklós; Lubotzky, Alexander; Pyber, László
2003
Counting hyperbolic manifolds. Zbl 1029.57021
Burger, M.; Gelander, T.; Lubotzky, A.; Mozes, S.
2002
The proalgebraic completion of rigid groups. Zbl 1059.20036
Bass, Hyman; Lubotzky, Alexander; Magid, Andy R.; Mozes, Shahar
2002
The expected number of random elements to generate a finite group. Zbl 1042.20047
Lubotzky, Alexander
2002
A group theoretical characterisation of S-arithmetic groups in higher rank semi-simple groups. Zbl 1012.22022
Lubotzky, A.; Venkataramana, T. N.
2002
Tree lattices. With appendices by H. Bass, L. Carbone, A. Lubotzky, G. Rosenberg, and J. Tits. Zbl 1053.20026
Bass, Hyman; Lubotzky, Alexander
2001
Rank-1 phenomena for mapping class groups. Zbl 1025.20023
Farb, Benson; Lubotzky, Alexander; Minsky, Yair
2001
The product replacement algorithm and Kazhdan’s property (T). Zbl 0980.20078
Lubotzky, Alexander; Pak, Igor
2001
Pro-finite presentations. Zbl 0985.20017
Lubotzky, Alexander
2001
Enumerating boundedly generated finite groups. Zbl 1052.20017
Lubotzky, Alexander
2001
Arithmetic structure of fundamental groups and actions of semisimple Lie groups. Zbl 0985.22005
Lubotzky, Alexander; Zimmer, Robert J.
2001
The word and Riemannian metrics on lattices of semisimple groups. Zbl 0988.22007
Lubotzky, Alexander; Mozes, Shahar; Raghunathan, M. S.
2000
Nonarithmetic superrigid groups: Counterexamples to Platonov’s conjecture. Zbl 0963.22005
Bass, Hyman; Lubotzky, Alexander
2000
Lattices of minimal covolume in $$\text{SL}_2$$ over local fields. Zbl 1026.22013
Lubotzky, A.; Weigel, Th.
1999
Random normal subgroups of free profinite groups. Zbl 0928.20027
Jarden, Moshe; Lubotzky, Alexander
1999
One for almost all: generation of $$\text{SL}(n,p)$$ by subsets of $$\text{SL}(n,\mathbb{Z})$$. Zbl 0979.20043
Lubotzky, Alexander
1999
Not every uniform tree covers Ramanujan graphs. Zbl 1024.05021
Lubotzky, Alexander; Nagnibeda, Tatiana
1998
A canonical arithmetic quotient for simple Lie group actions. Zbl 0946.22006
Lubotzky, Alexander; Zimmer, Robert J.
1998
Free quotients and the first Betti number of some hyperbolic manifolds. Zbl 0876.22015
Lubotzky, Alexander
1996
Eigenvalues of the Laplacian, the first Betti number and the congruence subgroup problem. Zbl 0885.11037
Lubotzky, Alexander
1996
Functional equations and uniformity for local zeta functions of nilpotent groups. Zbl 0864.20020
Du Sautoy, Marcus P. F.; Lubotzky, Alexander
1996
Powers in finitely generated groups. Zbl 0871.20038
Hrushovski, E.; Kropholler, P. H.; Lubotzky, A.; Shalev, A.
1996
Discrete groups of slow subgroup growth. Zbl 0877.20019
Lubotzky, Alexander; Pyber, László; Shalev, Aner
1996
Subgroup growth and congruence subgroups. Zbl 0848.20036
Lubotzky, Alexander
1995
Cayley graphs: Eigenvalues, expanders and random walks. Zbl 0835.05033
Lubotzky, Alexander
1995
...and 48 more Documents
all top 5

### Cited by 2,017 Authors

 84 Lubotzky, Alexander 43 Shalev, Aner 29 Lucchini, Andrea 23 Shumyatsky, Pavel 22 Guralnick, Robert Michael 21 Liebeck, Martin Walter 20 Kassabov, Martin 18 Pyber, László 16 Alon, Noga M. 16 Jaikin-Zapirain, Andrei 15 Klopsch, Benjamin 14 Zalesskii, Pavel 13 Gelander, Tsachik 13 Kantor, William M. 13 Khukhro, Evgeniĭ I. 13 Segal, Daniel 12 Bourgain, Jean 12 Larsen, Michael Jeffrey 12 Linial, Nathan 12 Mann, Avinoam 12 Rapinchuk, Andrei S. 11 Gamburd, Alexander 11 Magid, Andy Roy 10 Abért, Miklós 10 Avni, Nir 10 Belolipetsky, Mikhail V. 10 Leuzinger, Enrico 10 Parzanchevski, Ori 10 Reid, Alan W. 9 Acciarri, Cristina 9 Bekka, Mohammed el Bachir 9 Bou-Rabee, Khalid 9 Bridson, Martin R. 9 Capdeboscq, Inna 9 Ershov, Mikhail V. 9 Grunewald, Fritz J. 9 Lackenby, Marc 9 Long, Darren D. 9 Margalit, Dan 9 Moravec, Primož 9 Nikolov, Nikolay Valeriev 9 Porti, Joan 9 Voll, Christopher 8 Azarov, Dmitriĭ Nikolaevich 8 Caprace, Pierre-Emmanuel 8 Glasner, Yair 8 Haran, Dan 8 Kaufman, Tali 8 Koberda, Thomas 8 Mason, Alexander W. 8 Meiri, Chen 8 Mozes, Shahar 8 Müller, Thomas W. 8 Sarnak, Peter Clive 8 Shusterman, Mark 8 Sikora, Adam S. 8 Tran, Anh Tuan 8 Valette, Alain 8 Wong, Kok Bin 7 Aramayona, Javier 7 Babai, László 7 de Cornulier, Yves 7 Detomi, Eloisa 7 Goldman, William M. 7 González-Meneses, Juan 7 González-Sánchez, Jon 7 Grigorchuk, Rostislav Ivanovich 7 Heusener, Michael 7 Jarden, Moshe 7 Ku, Cheng Yeaw 7 Kunyavskiĭ, Boris Èmmanuilovich 7 Leedham-Green, Charles R. 7 McReynolds, David Ben 7 Mohar, Bojan 7 Myasnikov, Alexei G. 7 O’Brien, Eamonn A. 7 Ozawa, Narutaka 7 Pak, Igor 7 Salehi Golsefidy, Alireza 7 Schlage-Puchta, Jan-Christoph 7 Shalom, Yehuda 7 Snopce, Ilir 7 Terras, Audrey Anne 7 Thom, Andreas Berthold 7 Traustason, Gunnar 7 Vdovina, Alina A. 6 Barnea, Yiftach 6 Bestvina, Mladen 6 Boston, Nigel 6 Breuillard, Emmanuel 6 Carbone, Lisa J. 6 Chatzidakis, Zoé Maria 6 Chung, Fan 6 Cioabă, Sebastian M. 6 Conder, Marston D. E. 6 Friedl, Stefan 6 Gorodnik, Alexander 6 Ioana, Adrian 6 Kapovich, Michael 6 Kochloukova, Dessislava Hristova ...and 1,917 more Authors
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### Cited in 301 Serials

 173 Journal of Algebra 130 Israel Journal of Mathematics 70 Transactions of the American Mathematical Society 64 Proceedings of the American Mathematical Society 54 Advances in Mathematics 47 Geometriae Dedicata 43 Duke Mathematical Journal 42 Inventiones Mathematicae 39 Journal of Group Theory 36 International Journal of Algebra and Computation 34 Geometry & Topology 30 Mathematische Zeitschrift 30 Groups, Geometry, and Dynamics 29 Communications in Algebra 29 Combinatorica 28 Geometric and Functional Analysis. GAFA 28 Algebraic & Geometric Topology 27 Journal of Pure and Applied Algebra 25 Mathematische Annalen 25 Linear Algebra and its Applications 24 Discrete Mathematics 22 Mathematical Proceedings of the Cambridge Philosophical Society 22 Journal of Combinatorial Theory. Series B 21 Bulletin of the American Mathematical Society. New Series 20 European Journal of Combinatorics 20 Annals of Mathematics. Second Series 19 Ergodic Theory and Dynamical Systems 19 Journal of the American Mathematical Society 18 Archiv der Mathematik 18 Journal of Functional Analysis 17 Annales de l’Institut Fourier 17 Journal of the European Mathematical Society (JEMS) 16 Siberian Mathematical Journal 15 Monatshefte für Mathematik 15 Theoretical Computer Science 14 Compositio Mathematica 14 Discrete & Computational Geometry 13 Journal für die Reine und Angewandte Mathematik 13 Random Structures & Algorithms 13 Journal of Topology and Analysis 12 Discrete Applied Mathematics 12 Journal of Number Theory 12 Topology and its Applications 12 Experimental Mathematics 12 Journal of Mathematical Sciences (New York) 12 The Electronic Journal of Combinatorics 11 The Annals of Probability 11 Comptes Rendus. Mathématique. Académie des Sciences, Paris 10 Communications in Mathematical Physics 10 Publications Mathématiques 10 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI 10 Journal of Algebraic Combinatorics 10 Combinatorics, Probability and Computing 10 Proceedings of the Steklov Institute of Mathematics 9 Graphs and Combinatorics 9 Forum of Mathematics, Sigma 8 Bulletin of the Australian Mathematical Society 8 Glasgow Mathematical Journal 8 Journal of Graph Theory 8 Finite Fields and their Applications 8 Transformation Groups 7 Information Processing Letters 7 Journal of Mathematical Physics 7 The Journal of Symbolic Logic 7 Manuscripta Mathematica 7 SIAM Journal on Computing 7 Journal of Knot Theory and its Ramifications 7 Computational Complexity 6 Linear and Multilinear Algebra 6 Mathematics of Computation 6 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 6 Bulletin of the London Mathematical Society 6 Journal of Combinatorial Theory. Series A 6 Journal of Computer and System Sciences 6 Michigan Mathematical Journal 6 Pacific Journal of Mathematics 6 Designs, Codes and Cryptography 6 Journal of the Australian Mathematical Society 5 Journal d’Analyse Mathématique 5 Mathematical Notes 5 Algebra and Logic 5 Commentarii Mathematici Helvetici 5 Illinois Journal of Mathematics 5 Journal of Computational and Applied Mathematics 5 Memoirs of the American Mathematical Society 5 Proceedings of the London Mathematical Society. Third Series 5 Journal of Complexity 5 Algorithmica 5 Information and Computation 5 Journal of Algebra and its Applications 5 Groups, Complexity, Cryptology 5 International Journal of Group Theory 4 Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg 4 Indiana University Mathematics Journal 4 Journal of the London Mathematical Society. Second Series 4 Proceedings of the Edinburgh Mathematical Society. Series II 4 SIAM Journal on Discrete Mathematics 4 Journal de Théorie des Nombres de Bordeaux 4 Journal of High Energy Physics 4 International Journal of Number Theory ...and 201 more Serials
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### Cited in 55 Fields

 1,163 Group theory and generalizations (20-XX) 498 Combinatorics (05-XX) 314 Topological groups, Lie groups (22-XX) 310 Number theory (11-XX) 293 Manifolds and cell complexes (57-XX) 150 Computer science (68-XX) 138 Algebraic geometry (14-XX) 108 Dynamical systems and ergodic theory (37-XX) 91 Probability theory and stochastic processes (60-XX) 76 Functional analysis (46-XX) 68 Differential geometry (53-XX) 52 Global analysis, analysis on manifolds (58-XX) 51 Information and communication theory, circuits (94-XX) 49 Functions of a complex variable (30-XX) 48 Nonassociative rings and algebras (17-XX) 46 Field theory and polynomials (12-XX) 46 Geometry (51-XX) 45 Associative rings and algebras (16-XX) 41 Mathematical logic and foundations (03-XX) 41 Algebraic topology (55-XX) 40 Abstract harmonic analysis (43-XX) 38 Linear and multilinear algebra; matrix theory (15-XX) 35 Several complex variables and analytic spaces (32-XX) 31 Quantum theory (81-XX) 28 $$K$$-theory (19-XX) 22 Measure and integration (28-XX) 22 Convex and discrete geometry (52-XX) 19 Operations research, mathematical programming (90-XX) 18 Operator theory (47-XX) 14 Commutative algebra (13-XX) 14 Numerical analysis (65-XX) 12 General topology (54-XX) 12 Statistical mechanics, structure of matter (82-XX) 11 Ordinary differential equations (34-XX) 10 Partial differential equations (35-XX) 9 Statistics (62-XX) 8 Potential theory (31-XX) 7 General and overarching topics; collections (00-XX) 7 Order, lattices, ordered algebraic structures (06-XX) 6 Approximations and expansions (41-XX) 5 Special functions (33-XX) 4 History and biography (01-XX) 4 Category theory; homological algebra (18-XX) 4 Difference and functional equations (39-XX) 4 Relativity and gravitational theory (83-XX) 4 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 4 Biology and other natural sciences (92-XX) 3 Calculus of variations and optimal control; optimization (49-XX) 2 Mechanics of particles and systems (70-XX) 1 General algebraic systems (08-XX) 1 Real functions (26-XX) 1 Sequences, series, summability (40-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Integral transforms, operational calculus (44-XX) 1 Integral equations (45-XX)

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