# zbMATH — the first resource for mathematics

Compute Distance To:
 Documents Indexed: 106 Publications since 1991, including 11 Books
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#### Co-Authors

 22 single-authored 20 Yu, Jie-Tai 16 Myasnikov, Alexei G. 12 Grigor’ev, Dmitriĭ Yur’evich 12 Kahrobaei, Delaram 8 Ushakov, Alexander S. 6 Kapovich, Ilya 5 Schupp, Paul E. 4 Di Crescenzo, Giovanni 4 Khodjaeva, Matluba 4 Mikhalëv, Aleksandr Aleksandrovich 3 Baumslag, Gilbert 3 Koupparis, Charalambos 3 Zapata, Gabriel 2 Bessonov, Mariya 2 Gilman, Robert H. 2 Gupta, Chander Kanta 2 Habeeb, Maggie E. 2 Makar-Limanov, Leonid G. 2 Rivin, Igor 2 Rosenberger, Gerhard 1 Baginski, Paul 1 Bahturin, Yuri 1 Bardakov, Valeriĭ Georgievich 1 Bassino, Frédérique 1 Borovik, Alexandre Vasilievich 1 Bromberg, Lisa 1 Chorna, Anastasiia 1 Cleary, Sean 1 Drensky, Vesselin 1 Fazio, Nelly 1 Fine, Benjamin L. 1 Geller, Katherine 1 Gerritzen, Lothar 1 Goldfeld, Dorian Morris 1 Gribov, Alexey V. 1 Gupta, Narain Datt 1 Gutierrez, Jaime 1 Kish, Laszlo B. 1 Kreuzer, Martin 1 Lam, Chi-Ming 1 Levitt, Gilbert 1 Lohrey, Markus 1 Miasnikov, Alexei D. 1 Moldenhauer, Anja I. S. 1 Moriah, Yoav 1 Mostashari, Ali 1 Najarian, Kayvan 1 Nicaud, Cyril 1 Nicolosi, Antonio R. 1 Nikolaev, Andrey R. 1 Osin, Denis V. 1 Skeith, William E. III 1 Sosnovski, Bianca 1 Tolstykh, Vladimir A. 1 Umirbaev, Ualbaĭ Utmakhanbetovich 1 van den Essen, Arno 1 van Rossum, Peter 1 Vdovina, Alina A. 1 Weil, Pascal 1 Wood, Alexander W.
all top 5

#### Serials

 10 Groups, Complexity, Cryptology 9 Journal of Algebra 6 Contemporary Mathematics 5 Journal of Pure and Applied Algebra 5 International Journal of Algebra and Computation 4 Proceedings of the American Mathematical Society 3 Communications in Algebra 3 Mathematical Proceedings of the Cambridge Philosophical Society 3 Archiv der Mathematik 2 Israel Journal of Mathematics 2 Transactions of the American Mathematical Society 2 International Journal of Foundations of Computer Science 2 Applicable Algebra in Engineering, Communication and Computing 1 Advances in Mathematics 1 Bulletin of the London Mathematical Society 1 Commentarii Mathematici Helvetici 1 Illinois Journal of Mathematics 1 Pacific Journal of Mathematics 1 Results in Mathematics 1 Semigroup Forum 1 Annals of Pure and Applied Logic 1 Journal of Symbolic Computation 1 Algebra Colloquium 1 Mathematical Research Letters 1 Mathematical Surveys and Monographs 1 CMS Books in Mathematics/Ouvrages de Mathématiques de la SMC 1 Mathematics in Computer Science 1 Journal of Mathematical Cryptology 1 Advanced Courses in Mathematics – CRM Barcelona 1 De Gruyter Proceedings in Mathematics
all top 5

#### Fields

 57 Group theory and generalizations (20-XX) 42 Information and communication theory, circuits (94-XX) 23 Computer science (68-XX) 19 Algebraic geometry (14-XX) 14 Commutative algebra (13-XX) 9 General and overarching topics; collections (00-XX) 8 Associative rings and algebras (16-XX) 8 Nonassociative rings and algebras (17-XX) 7 Number theory (11-XX) 6 Mathematical logic and foundations (03-XX) 4 Manifolds and cell complexes (57-XX) 2 Combinatorics (05-XX) 2 Linear and multilinear algebra; matrix theory (15-XX) 2 Probability theory and stochastic processes (60-XX) 1 Field theory and polynomials (12-XX) 1 Abstract harmonic analysis (43-XX) 1 Statistics (62-XX) 1 Biology and other natural sciences (92-XX)

#### Citations contained in zbMATH Open

80 Publications have been cited 739 times in 409 Documents Cited by Year
Generic-case complexity, decision problems in group theory, and random walks. Zbl 1041.20021
Kapovich, Ilya; Myasnikov, Alexei; Schupp, Paul; Shpilrain, Vladimir
2003
Group-based cryptography. Zbl 1248.94004
Myasnikov, Alexei; Shpilrain, Vladimir; Ushakov, Alexander
2008
Non-commutative cryptography and complexity of group-theoretic problems. With an appendix by Natalia Mosina. Zbl 1248.94006
Myasnikov, Alexei; Shpilrain, Vladimir; Ushakov, Alexander
2011
Average-case complexity and decision problems in group theory. Zbl 1065.20044
Kapovich, Ilya; Myasnikov, Alexei; Schupp, Paul; Shpilrain, Vladimir
2005
Combinatorial methods. Free groups, polynomials, and free algebras. Zbl 1039.16024
Mikhalev, Alexander A.; Shpilrain, Vladimir; Yu, Jie-Tai
2004
Generic properties of Whitehead’s algorithm and isomorphism rigidity of random one-relator groups. Zbl 1149.20028
Kapovich, Ilya; Schupp, Paul; Shpilrain, Vladimir
2006
Recognizing automorphisms of the free groups. Zbl 0802.20024
1994
Combinatorial group theory and public key cryptography. Zbl 1104.94038
2006
On the palindromic and primitive widths of a free group. Zbl 1085.20011
2005
Polynomial automorphisms and Gröbner reductions. Zbl 0899.13029
1997
Automorphic orbits in free groups. Zbl 1035.20019
2003
Thompson’s group and public key cryptography. Zbl 1126.68416
2005
Open problems in combinatorial group theory. Second edition. Zbl 1065.20042
Baumslag, Gilbert; Myasnikov, Alexei G.; Shpilrain, Vladimir
2002
Some combinatorial questions about polynomial mappings. Zbl 0899.13009
van den Essen, Arno; Shpilrain, Vladimir
1997
Affine varieties with equivalent cylinders. Zbl 1067.14064
2002
On generators of $$L/R^ 2$$ Lie algebras. Zbl 0794.17004
1993
Representing braids by automorphisms. Zbl 1024.20036
2001
Embeddings of curves in the plane. Zbl 0964.14025
1999
Generalized primitive elements of a free group. Zbl 0913.20016
1998
Cryptanalysis of Stickel’s key exchange scheme. Zbl 1142.94360
2008
A new key exchange protocol based on the decomposition problem. Zbl 1207.94063
2006
Random subgroups of braid groups: An approach to cryptanalysis of a braid group based cryptographic protocol. Zbl 1151.94554
Myasnikov, Alexei; Shpilrain, Vladimir; Ushakov, Alexander
2006
Polynomial Retracts and the Jacobian Conjecture. Zbl 0944.13011
2000
Tropical cryptography. Zbl 1301.94114
2014
Public key exchange using semidirect product of (semi)groups. Zbl 1356.94059
Habeeb, Maggie; Kahrobaei, Delaram; Koupparis, Charalambos; Shpilrain, Vladimir
2013
Public key exchange using matrices over group rings. Zbl 1290.94099
Kahrobaei, Delaram; Koupparis, Charalambos; Shpilrain, Vladimir
2013
The conjugacy search problem in public key cryptography: unnecessary and insufficient. Zbl 1104.94037
2006
Measuring sets in infinite groups. Zbl 1022.20010
Borovik, Alexandre V.; Myasnikov, Alexei G.; Shpilrain, Vladimir
2002
On generators of polynomial algebras in two commuting or non-commuting variables. Zbl 0932.16027
1998
Test elements for endomorphisms of free groups and algebras. Zbl 0839.20044
1995
Authentication from matrix conjugation. Zbl 1191.94104
2009
Densities in free groups and $$\mathbb{Z}^k$$, visible points and test elements. Zbl 1132.20017
Kapovich, Ilya; Rivin, Igor; Schupp, Paul; Shpilrain, Vladimir
2007
The stable equivalence and cancellation problems. Zbl 1063.14077
Makar-Limanov, Leonid; van Rossum, Peter; Shpilrain, Vladimir; Yu, Jie-Tai
2004
On the rank of an element of a free Lie algebra. Zbl 0845.17007
1995
Navigating in the Cayley graph of $$\mathrm{SL}_2(\mathbb F_p)$$ and applications to hashing. Zbl 1420.94042
Bromberg, Lisa; Shpilrain, Vladimir; Vdovina, Alina
2017
Authentication schemes from actions on graphs, groups, or rings. Zbl 1236.94076
2010
Using the subgroup membership search problem in public key cryptography. Zbl 1207.94064
2006
A practical attack on a braid group based cryptographic protocol. Zbl 1145.94448
Myasnikov, Alexei; Shpilrain, Vladimir; Ushakov, Alexander
2005
Embeddings of hypersurfaces in affine spaces. Zbl 1064.14076
2001
Open problems in combinatorial group theory. Zbl 0976.20023
Baumslag, Gilbert; Myasnikov, Alexei G.; Shpilrain, Vladimir
1999
Using semidirect product of (semi)groups in public key cryptography. Zbl 1353.94055
2016
Search and witness problems in group theory. Zbl 1222.20024
2010
Translation equivalence in free groups. Zbl 1119.20037
Kapovich, Ilya; Levitt, Gilbert; Schupp, Paul; Shpilrain, Vladimir
2007
Nielsen’s commutator test for two-generator groups. Zbl 0793.20023
1993
Automorphisms of $$F/R'$$ groups. Zbl 0801.20010
1991
On two-generator subgroups in $$\mathrm{SL}_2(\mathbb{Z})$$, $$\mathrm{SL}_2(\mathbb{Q})$$, and $$\mathrm{SL}_2(\mathbb{R})$$. Zbl 1406.20046
Chorna, Anastasiia; Geller, Katherine; Shpilrain, Vladimir
2017
A secret sharing scheme based on group presentations and the word problem. Zbl 1278.94051
Habeeb, Maggie; Kahrobaei, Delaram; Shpilrain, Vladimir
2012
Using decision problems in public key cryptography. Zbl 1156.94379
2009
Some metric properties of automorphisms of groups. Zbl 1112.20036
2006
Test polynomial, retracts, and the Jacobian conjecture. Zbl 1073.14076
2005
Assessing security of some group based cryptosystems. Zbl 1161.68486
2004
Factor algebras of free algebras: on a problem of G. Bergman. Zbl 1035.16016
2003
On the Andrews-Curtis equivalence. Zbl 1010.20019
Myasnikov, Alexei D.; Myasnikov, Alexei G.; Shpilrain, Vladimir
2002
On endomorphisms of free algebras. Zbl 0946.17001
Mikhalev, Alexander A.; Shpilrain, Vladimir; Yu, Jie-Tai
1999
Fixed points of endomorphisms of a free metabelian group. Zbl 0894.20027
1998
Efficient and secure delegation to a single malicious server: exponentiation over non-abelian groups. Zbl 1398.94110
Di Crescenzo, Giovanni; Kahrobaei, Delaram; Khodjaeva, Matluba; Shpilrain, Vladimir
2018
Generalized learning problems and applications to non-commutative cryptography. (Extended abstract). Zbl 1298.94080
Baumslag, Gilbert; Fazio, Nelly; Nicolosi, Antonio R.; Shpilrain, Vladimir; Skeith, William E. III
2011
Equivalence of polynomials under automorphisms of $$K[x,y]$$. Zbl 1106.14051
Makar-Limanov, Leonid; Shpilrain, Vladimir; Yu, Jie-Tai
2007
On isomorphism of Lie algebras with one defining relation. Zbl 1107.17002
Mikhalev, Alexander A.; Shpilrain, Vladimir; Umirbaev, Ualbai U.
2004
Magnus embeddings for semigroups. Zbl 0858.20051
1996
Lifting automorphisms: A survey. Zbl 0841.20034
1995
On monomorphisms of free groups. Zbl 0823.20030
1995
Compositions of linear functions and applications to hashing. Zbl 1353.94073
2016
Recognizing and parametrizing curves isomorphic to a line. Zbl 1134.13024
Lam, Chi-Ming; Shpilrain, Vladimir; Yu, Jie-Tai
2007
Counting primitive elements of a free group. Zbl 1077.20046
2005
Peak reduction technique in commutative algebra: a survey. Zbl 1070.14062
2000
An inverse function theorem for free associative algebras of rank two. Zbl 0793.16015
1992
Efficient and secure delegation of exponentiation in general groups to a single malicious server. Zbl 07268450
Di Crescenzo, Giovanni; Khodjaeva, Matluba; Kahrobaei, Delaram; Shpilrain, Vladimir
2020
Complexity and randomness in group theory. GAGTA book 1. Zbl 07205680
Bassino, Frédérique; Kapovich, Ilya; Lohrey, Markus; Miasnikov, Alexei; Nicaud, Cyril; Nikolaev, Andrey; Rivin, Igor; Shpilrain, Vladimir; Ushakov, Alexander; Weil, Pascal
2020
Tropical cryptography. II: Extensions by homomorphisms. Zbl 1451.14179
2019
A CCA secure cryptosystem using matrices over group rings. Zbl 1345.94071
Kahrobaei, Delaram; Koupparis, Charalambos; Shpilrain, Vladimir
2015
Yao’s millionaires’ problem and decoy-based public key encryption by classical physics. Zbl 1302.94049
2014
Secrecy without one-way functions. Zbl 1290.94080
2013
No-leak authentication by the Sherlock Holmes method. Zbl 1272.94081
2012
Sublinear time algorithms in the theory of groups and semigroups. Zbl 1234.20044
2010
Affine algebraic geometry. Contributions of the special session on affine algebraic geometry at the 1st joint AMS-RSME meeting, Seville, Spain, June 18–21, 2003. Zbl 1058.14001
Gutierrez, Jaime (ed.); Shpilrain, Vladimir (ed.); Yu, Jie-Tai (ed.)
2005
Combinatorial problems about free groups and algebras. Zbl 1064.20025
Mikhalev, Alexander A.; Shpilrain, Vladimir; Yu, Jie-Tai
2000
On the density of the set of generators of a polynomial algebra. Zbl 0957.13017
Drensky, Vesselin; Shpilrain, Vladimir; Yu, Jie-Tai
2000
Automorphisms of one-relator groups. Zbl 0932.20045
1999
On Lie algebras with wild automorphisms. Zbl 0837.17010
1995
Efficient and secure delegation of exponentiation in general groups to a single malicious server. Zbl 07268450
Di Crescenzo, Giovanni; Khodjaeva, Matluba; Kahrobaei, Delaram; Shpilrain, Vladimir
2020
Complexity and randomness in group theory. GAGTA book 1. Zbl 07205680
Bassino, Frédérique; Kapovich, Ilya; Lohrey, Markus; Miasnikov, Alexei; Nicaud, Cyril; Nikolaev, Andrey; Rivin, Igor; Shpilrain, Vladimir; Ushakov, Alexander; Weil, Pascal
2020
Tropical cryptography. II: Extensions by homomorphisms. Zbl 1451.14179
2019
Efficient and secure delegation to a single malicious server: exponentiation over non-abelian groups. Zbl 1398.94110
Di Crescenzo, Giovanni; Kahrobaei, Delaram; Khodjaeva, Matluba; Shpilrain, Vladimir
2018
Navigating in the Cayley graph of $$\mathrm{SL}_2(\mathbb F_p)$$ and applications to hashing. Zbl 1420.94042
Bromberg, Lisa; Shpilrain, Vladimir; Vdovina, Alina
2017
On two-generator subgroups in $$\mathrm{SL}_2(\mathbb{Z})$$, $$\mathrm{SL}_2(\mathbb{Q})$$, and $$\mathrm{SL}_2(\mathbb{R})$$. Zbl 1406.20046
Chorna, Anastasiia; Geller, Katherine; Shpilrain, Vladimir
2017
Using semidirect product of (semi)groups in public key cryptography. Zbl 1353.94055
2016
Compositions of linear functions and applications to hashing. Zbl 1353.94073
2016
A CCA secure cryptosystem using matrices over group rings. Zbl 1345.94071
Kahrobaei, Delaram; Koupparis, Charalambos; Shpilrain, Vladimir
2015
Tropical cryptography. Zbl 1301.94114
2014
Yao’s millionaires’ problem and decoy-based public key encryption by classical physics. Zbl 1302.94049
2014
Public key exchange using semidirect product of (semi)groups. Zbl 1356.94059
Habeeb, Maggie; Kahrobaei, Delaram; Koupparis, Charalambos; Shpilrain, Vladimir
2013
Public key exchange using matrices over group rings. Zbl 1290.94099
Kahrobaei, Delaram; Koupparis, Charalambos; Shpilrain, Vladimir
2013
Secrecy without one-way functions. Zbl 1290.94080
2013
A secret sharing scheme based on group presentations and the word problem. Zbl 1278.94051
Habeeb, Maggie; Kahrobaei, Delaram; Shpilrain, Vladimir
2012
No-leak authentication by the Sherlock Holmes method. Zbl 1272.94081
2012
Non-commutative cryptography and complexity of group-theoretic problems. With an appendix by Natalia Mosina. Zbl 1248.94006
Myasnikov, Alexei; Shpilrain, Vladimir; Ushakov, Alexander
2011
Generalized learning problems and applications to non-commutative cryptography. (Extended abstract). Zbl 1298.94080
Baumslag, Gilbert; Fazio, Nelly; Nicolosi, Antonio R.; Shpilrain, Vladimir; Skeith, William E. III
2011
Authentication schemes from actions on graphs, groups, or rings. Zbl 1236.94076
2010
Search and witness problems in group theory. Zbl 1222.20024
2010
Sublinear time algorithms in the theory of groups and semigroups. Zbl 1234.20044
2010
Authentication from matrix conjugation. Zbl 1191.94104
2009
Using decision problems in public key cryptography. Zbl 1156.94379
2009
Group-based cryptography. Zbl 1248.94004
Myasnikov, Alexei; Shpilrain, Vladimir; Ushakov, Alexander
2008
Cryptanalysis of Stickel’s key exchange scheme. Zbl 1142.94360
2008
Densities in free groups and $$\mathbb{Z}^k$$, visible points and test elements. Zbl 1132.20017
Kapovich, Ilya; Rivin, Igor; Schupp, Paul; Shpilrain, Vladimir
2007
Translation equivalence in free groups. Zbl 1119.20037
Kapovich, Ilya; Levitt, Gilbert; Schupp, Paul; Shpilrain, Vladimir
2007
Equivalence of polynomials under automorphisms of $$K[x,y]$$. Zbl 1106.14051
Makar-Limanov, Leonid; Shpilrain, Vladimir; Yu, Jie-Tai
2007
Recognizing and parametrizing curves isomorphic to a line. Zbl 1134.13024
Lam, Chi-Ming; Shpilrain, Vladimir; Yu, Jie-Tai
2007
Generic properties of Whitehead’s algorithm and isomorphism rigidity of random one-relator groups. Zbl 1149.20028
Kapovich, Ilya; Schupp, Paul; Shpilrain, Vladimir
2006
Combinatorial group theory and public key cryptography. Zbl 1104.94038
2006
A new key exchange protocol based on the decomposition problem. Zbl 1207.94063
2006
Random subgroups of braid groups: An approach to cryptanalysis of a braid group based cryptographic protocol. Zbl 1151.94554
Myasnikov, Alexei; Shpilrain, Vladimir; Ushakov, Alexander
2006
The conjugacy search problem in public key cryptography: unnecessary and insufficient. Zbl 1104.94037
2006
Using the subgroup membership search problem in public key cryptography. Zbl 1207.94064
2006
Some metric properties of automorphisms of groups. Zbl 1112.20036
2006
Average-case complexity and decision problems in group theory. Zbl 1065.20044
Kapovich, Ilya; Myasnikov, Alexei; Schupp, Paul; Shpilrain, Vladimir
2005
On the palindromic and primitive widths of a free group. Zbl 1085.20011
2005
Thompson’s group and public key cryptography. Zbl 1126.68416
2005
A practical attack on a braid group based cryptographic protocol. Zbl 1145.94448
Myasnikov, Alexei; Shpilrain, Vladimir; Ushakov, Alexander
2005
Test polynomial, retracts, and the Jacobian conjecture. Zbl 1073.14076
2005
Counting primitive elements of a free group. Zbl 1077.20046
2005
Affine algebraic geometry. Contributions of the special session on affine algebraic geometry at the 1st joint AMS-RSME meeting, Seville, Spain, June 18–21, 2003. Zbl 1058.14001
Gutierrez, Jaime (ed.); Shpilrain, Vladimir (ed.); Yu, Jie-Tai (ed.)
2005
Combinatorial methods. Free groups, polynomials, and free algebras. Zbl 1039.16024
Mikhalev, Alexander A.; Shpilrain, Vladimir; Yu, Jie-Tai
2004
The stable equivalence and cancellation problems. Zbl 1063.14077
Makar-Limanov, Leonid; van Rossum, Peter; Shpilrain, Vladimir; Yu, Jie-Tai
2004
Assessing security of some group based cryptosystems. Zbl 1161.68486
2004
On isomorphism of Lie algebras with one defining relation. Zbl 1107.17002
Mikhalev, Alexander A.; Shpilrain, Vladimir; Umirbaev, Ualbai U.
2004
Generic-case complexity, decision problems in group theory, and random walks. Zbl 1041.20021
Kapovich, Ilya; Myasnikov, Alexei; Schupp, Paul; Shpilrain, Vladimir
2003
Automorphic orbits in free groups. Zbl 1035.20019
2003
Factor algebras of free algebras: on a problem of G. Bergman. Zbl 1035.16016
2003
Open problems in combinatorial group theory. Second edition. Zbl 1065.20042
Baumslag, Gilbert; Myasnikov, Alexei G.; Shpilrain, Vladimir
2002
Affine varieties with equivalent cylinders. Zbl 1067.14064
2002
Measuring sets in infinite groups. Zbl 1022.20010
Borovik, Alexandre V.; Myasnikov, Alexei G.; Shpilrain, Vladimir
2002
On the Andrews-Curtis equivalence. Zbl 1010.20019
Myasnikov, Alexei D.; Myasnikov, Alexei G.; Shpilrain, Vladimir
2002
Representing braids by automorphisms. Zbl 1024.20036
2001
Embeddings of hypersurfaces in affine spaces. Zbl 1064.14076
2001
Polynomial Retracts and the Jacobian Conjecture. Zbl 0944.13011
2000
Peak reduction technique in commutative algebra: a survey. Zbl 1070.14062
2000
Combinatorial problems about free groups and algebras. Zbl 1064.20025
Mikhalev, Alexander A.; Shpilrain, Vladimir; Yu, Jie-Tai
2000
On the density of the set of generators of a polynomial algebra. Zbl 0957.13017
Drensky, Vesselin; Shpilrain, Vladimir; Yu, Jie-Tai
2000
Embeddings of curves in the plane. Zbl 0964.14025
1999
Open problems in combinatorial group theory. Zbl 0976.20023
Baumslag, Gilbert; Myasnikov, Alexei G.; Shpilrain, Vladimir
1999
On endomorphisms of free algebras. Zbl 0946.17001
Mikhalev, Alexander A.; Shpilrain, Vladimir; Yu, Jie-Tai
1999
Automorphisms of one-relator groups. Zbl 0932.20045
1999
Generalized primitive elements of a free group. Zbl 0913.20016
1998
On generators of polynomial algebras in two commuting or non-commuting variables. Zbl 0932.16027
1998
Fixed points of endomorphisms of a free metabelian group. Zbl 0894.20027
1998
Polynomial automorphisms and Gröbner reductions. Zbl 0899.13029
1997
Some combinatorial questions about polynomial mappings. Zbl 0899.13009
van den Essen, Arno; Shpilrain, Vladimir
1997
Magnus embeddings for semigroups. Zbl 0858.20051
1996
Test elements for endomorphisms of free groups and algebras. Zbl 0839.20044
1995
On the rank of an element of a free Lie algebra. Zbl 0845.17007
1995
Lifting automorphisms: A survey. Zbl 0841.20034
1995
On monomorphisms of free groups. Zbl 0823.20030
1995
On Lie algebras with wild automorphisms. Zbl 0837.17010
1995
Recognizing automorphisms of the free groups. Zbl 0802.20024
1994
On generators of $$L/R^ 2$$ Lie algebras. Zbl 0794.17004
1993
Nielsen’s commutator test for two-generator groups. Zbl 0793.20023
1993
An inverse function theorem for free associative algebras of rank two. Zbl 0793.16015
1992
Automorphisms of $$F/R'$$ groups. Zbl 0801.20010
1991
all top 5

#### Cited by 411 Authors

 39 Yu, Jie-Tai 34 Shpilrain, Vladimir 22 Rybalov, Aleksandr Nikolaevich 21 Myasnikov, Alexei G. 19 Roman’kov, Vitaly Anatol’evich 14 Drensky, Vesselin 14 Ushakov, Alexander S. 12 Mikhalëv, Aleksandr Aleksandrovich 11 Schupp, Paul E. 10 Kahrobaei, Delaram 10 Kapovich, Ilya 9 Bardakov, Valeriĭ Georgievich 7 Grigor’ev, Dmitriĭ Yur’evich 7 Lee, Donghi 6 Umirbaev, Ualbaĭ Utmakhanbetovich 6 Weil, Pascal 5 Ekici, Naime 5 Gongopadhyay, Krishnendu 5 Hirschfeldt, Denis Roman 5 Jockusch, Carl G. jun. 5 Klimakov, A. V. 5 Timoshenko, Evgeniĭ Iosifovich 5 Weiß, Armin 4 Climent, Joan-Josep 4 Fine, Benjamin L. 4 Gilman, Robert H. 4 Ivanov, Sergei Vladimirovich 4 Jelonek, Zbigniew 4 Kanel’-Belov, Alekseĭ Yakovlevich 4 Osin, Denis V. 4 Silva, Pedro V. 4 Tsaban, Boaz 3 Abdulrahim, Mohammad N. 3 Bassino, Frédérique 3 Ciobanu, Laura 3 Diekert, Volker 3 El Kahoui, M’hammed 3 Elder, Murray J. 3 Gong, Sheng-Jun 3 Gupta, Chander Kanta 3 Haubold, Niko 3 Igusa, Gregory 3 Kambites, Mark 3 Kotov, Matvei 3 Lohrey, Markus 3 Makar-Limanov, Leonid G. 3 Navarro, Pedro R. 3 Nicaud, Cyril 3 Poloni, Pierre-Marie 3 Remeslennikov, Vladimir Nikanorovich 3 Rosenberger, Gerhard 3 Sapir, Mark Valentinovich 3 Tolstykh, Vladimir A. 3 Tortosa, Leandro 3 Ventura Capell, Enric 2 Al Tahan, Madeline 2 Astor, Eric P. 2 Bandman, Tatiana M. 2 Baumslag, Gilbert 2 Bokut, Leonid A. 2 Borovik, Alexandre Vasilievich 2 Brandenbursky, Michael 2 Cavaleri, Matteo 2 David, Julien 2 Davvaz, Bijan 2 Di Crescenzo, Giovanni 2 Downey, Rodney Graham 2 Eftekhari, Mohammad 2 El Houari, Hassan 2 Erofeev, S. Yu. 2 Esbelin, Henri-Alex 2 Fazio, Nelly 2 Fink, Elisabeth 2 Fleischmann, Peter 2 Furter, Jean-Philippe 2 Gaynullina, Alina R. 2 Gryak, Jonathan 2 Gupta, Indivar 2 Gutan, Marin 2 Haralick, Robert M. 2 Kalka, Arkadius G. 2 Kharlampovich, Olga G. 2 Khodjaeva, Matluba 2 Khoussainov, Bakhadyr M. 2 Kniesburges, Sebastian 2 Koutsopoulos, Andreas 2 Kunyavskiĭ, Boris Èmmanuilovich 2 Kuroda, Shigeru 2 Lam, Chi-Ming 2 Lempp, Steffen 2 Marcinkowski, Michał 2 Menshov, Anton 2 Mikhalchishina, Yuliya A. 2 Mikhalëv, Aleksandr Vasil’evich 2 Monico, Chris 2 Moser-Jauslin, Lucy 2 Nicolosi, Antonio R. 2 Nikolaev, Andrey R. 2 Öğüşlü, Nazar Şahin 2 Ostheimer, Gretchen ...and 311 more Authors
all top 5

#### Cited in 108 Serials

 48 Journal of Algebra 30 International Journal of Algebra and Computation 24 Communications in Algebra 23 Groups, Complexity, Cryptology 20 Prikladnaya Diskretnaya Matematika 13 Journal of Pure and Applied Algebra 12 Applicable Algebra in Engineering, Communication and Computing 10 Proceedings of the American Mathematical Society 9 Israel Journal of Mathematics 8 Algebra and Logic 8 Journal of Mathematical Cryptology 7 The Journal of Symbolic Logic 7 Journal of Mathematical Sciences (New York) 6 Designs, Codes and Cryptography 5 Mathematical Proceedings of the Cambridge Philosophical Society 5 Illinois Journal of Mathematics 5 Theoretical Computer Science 5 Journal of Symbolic Computation 5 Proceedings of the Indian Academy of Sciences. Mathematical Sciences 5 Journal of Algebra and its Applications 4 Advances in Mathematics 4 Siberian Mathematical Journal 4 Transactions of the American Mathematical Society 4 Theory of Computing Systems 4 International Journal of Group Theory 3 Archiv der Mathematik 3 Inventiones Mathematicae 3 Journal of Cryptology 3 Algebra Colloquium 3 Journal of the European Mathematical Society (JEMS) 3 Algebraic & Geometric Topology 3 Groups, Geometry, and Dynamics 3 Bulletin of Mathematical Sciences 2 Bulletin of the Australian Mathematical Society 2 Moscow University Mathematics Bulletin 2 Journal of the Mathematical Society of Japan 2 Mathematische Annalen 2 Semigroup Forum 2 Topology and its Applications 2 Algorithmica 2 International Journal of Foundations of Computer Science 2 Geometric and Functional Analysis. GAFA 2 Proceedings of the National Academy of Sciences of the United States of America 2 Transformation Groups 2 Geometry & Topology 2 Lobachevskii Journal of Mathematics 2 Journal of the Australian Mathematical Society 2 Sibirskie Èlektronnye Matematicheskie Izvestiya 2 Advances in Mathematics of Communications 2 Computability 1 Rocky Mountain Journal of Mathematics 1 Mathematics of Computation 1 Annales de l’Institut Fourier 1 Commentarii Mathematici Helvetici 1 Computing 1 Fundamenta Mathematicae 1 Geometriae Dedicata 1 International Journal of Mathematics and Mathematical Sciences 1 Journal of Computer and System Sciences 1 Journal of the London Mathematical Society. Second Series 1 Journal für die Reine und Angewandte Mathematik 1 Michigan Mathematical Journal 1 European Journal of Combinatorics 1 Advances in Applied Mathematics 1 Annals of Pure and Applied Logic 1 Computer Aided Geometric Design 1 Discrete & Computational Geometry 1 Forum Mathematicum 1 Science in China. Series A 1 Random Structures & Algorithms 1 L’Enseignement Mathématique. 2e Série 1 International Journal of Computer Mathematics 1 Bulletin of the American Mathematical Society. New Series 1 Expositiones Mathematicae 1 Journal of Knot Theory and its Ramifications 1 Cybernetics and Systems Analysis 1 Computational Complexity 1 Experimental Mathematics 1 Journal of Algebraic Geometry 1 Russian Journal of Mathematical Physics 1 St. Petersburg Mathematical Journal 1 The New York Journal of Mathematics 1 Selecta Mathematica. New Series 1 Izvestiya: Mathematics 1 Journal of Mathematical Chemistry 1 Journal of Group Theory 1 Wuhan University Journal of Natural Sciences (WUJNS) 1 Journal of Discrete Mathematical Sciences & Cryptography 1 Annals of Mathematics. Second Series 1 LMS Journal of Computation and Mathematics 1 RAIRO. Theoretical Informatics and Applications 1 Communications in Contemporary Mathematics 1 Journal of Mathematical Logic 1 Journal of Applied Mathematics 1 Entropy 1 Central European Journal of Mathematics 1 Oberwolfach Reports 1 Chebyshevskiĭ Sbornik 1 Mathematics in Computer Science 1 Frontiers of Mathematics in China ...and 8 more Serials
all top 5

#### Cited in 33 Fields

 209 Group theory and generalizations (20-XX) 91 Computer science (68-XX) 80 Information and communication theory, circuits (94-XX) 61 Algebraic geometry (14-XX) 43 Mathematical logic and foundations (03-XX) 42 Commutative algebra (13-XX) 40 Nonassociative rings and algebras (17-XX) 39 Associative rings and algebras (16-XX) 22 Manifolds and cell complexes (57-XX) 20 Combinatorics (05-XX) 16 Number theory (11-XX) 11 Dynamical systems and ergodic theory (37-XX) 7 Probability theory and stochastic processes (60-XX) 6 Linear and multilinear algebra; matrix theory (15-XX) 5 Quantum theory (81-XX) 4 General algebraic systems (08-XX) 4 Field theory and polynomials (12-XX) 4 Abstract harmonic analysis (43-XX) 4 Differential geometry (53-XX) 3 Category theory; homological algebra (18-XX) 3 Algebraic topology (55-XX) 3 Operations research, mathematical programming (90-XX) 2 Topological groups, Lie groups (22-XX) 2 Functions of a complex variable (30-XX) 1 General and overarching topics; collections (00-XX) 1 History and biography (01-XX) 1 Order, lattices, ordered algebraic structures (06-XX) 1 Measure and integration (28-XX) 1 Ordinary differential equations (34-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Functional analysis (46-XX) 1 Numerical analysis (65-XX) 1 Relativity and gravitational theory (83-XX)