Lucchini, Andrea; Sabatini, Luca; Stanojkovski, Mima On finite \(d\)-maximal groups. (English) Zbl 07815316 Bull. Lond. Math. Soc. 56, No. 3, 1054-1070 (2024). MSC: 20D10 20D15 20D45 20F05 20F16 PDFBibTeX XMLCite \textit{A. Lucchini} et al., Bull. Lond. Math. Soc. 56, No. 3, 1054--1070 (2024; Zbl 07815316) Full Text: DOI arXiv OA License
Lucchini, Andrea; Malinin, Dmitry IBIS soluble linear groups. (English) Zbl 07790902 Commun. Algebra 52, No. 1, 457-465 (2024). Reviewer: Alexander Hulpke (Fort Collins) MSC: 20B15 20D10 PDFBibTeX XMLCite \textit{A. Lucchini} and \textit{D. Malinin}, Commun. Algebra 52, No. 1, 457--465 (2024; Zbl 07790902) Full Text: DOI arXiv
Lucchini, Andrea; Thakkar, Dhara The minimum generating set problem. (English) Zbl 07783370 J. Algebra 640, 117-128 (2024). Reviewer: Enrico Jabara (Venezia) MSC: 20F05 20-08 20D60 PDFBibTeX XMLCite \textit{A. Lucchini} and \textit{D. Thakkar}, J. Algebra 640, 117--128 (2024; Zbl 07783370) Full Text: DOI arXiv
Lucchini, Andrea; Spiga, Pablo Finite groups with independent generating sets of only two sizes. (English) Zbl 1526.20049 Bull. Aust. Math. Soc. 108, No. 3, 449-458 (2023). Reviewer: Enrico Jabara (Venezia) MSC: 20F05 20D60 20E34 PDFBibTeX XMLCite \textit{A. Lucchini} and \textit{P. Spiga}, Bull. Aust. Math. Soc. 108, No. 3, 449--458 (2023; Zbl 1526.20049) Full Text: DOI OA License
Lucchini, Andrea; Spiga, Pablo Hypermaps over non-abelian simple groups and strongly symmetric generating sets. (English) Zbl 1523.20011 Electron. J. Comb. 30, No. 3, Research Paper P3.13, 8 p. (2023). Reviewer: John D. Dixon (Ottawa) MSC: 20B25 05C25 20D05 PDFBibTeX XMLCite \textit{A. Lucchini} and \textit{P. Spiga}, Electron. J. Comb. 30, No. 3, Research Paper P3.13, 8 p. (2023; Zbl 1523.20011) Full Text: DOI arXiv
Lucchini, Andrea; Nemmi, Daniele Semiregularity and connectivity of the non-\(\mathfrak{F}\) graph of a finite group. (English) Zbl 1520.20054 J. Algebra Appl. 22, No. 9, Article ID 2350190, 14 p. (2023). MSC: 20D60 05C25 PDFBibTeX XMLCite \textit{A. Lucchini} and \textit{D. Nemmi}, J. Algebra Appl. 22, No. 9, Article ID 2350190, 14 p. (2023; Zbl 1520.20054) Full Text: DOI arXiv
Freedman, Saul D.; Lucchini, Andrea; Nemmi, Daniele; Roney-Dougal, Colva M. Finite groups satisfying the independence property. (English) Zbl 1516.20052 Int. J. Algebra Comput. 33, No. 3, 509-545 (2023). Reviewer: Enrico Jabara (Venezia) MSC: 20D60 20D10 20D05 PDFBibTeX XMLCite \textit{S. D. Freedman} et al., Int. J. Algebra Comput. 33, No. 3, 509--545 (2023; Zbl 1516.20052) Full Text: DOI arXiv
Dalla Volta, Francesca; Lucchini, Andrea The \(A\)-Möbius function of a finite group. (English) Zbl 1515.20106 Ars Math. Contemp. 23, No. 3, Paper No. 8, 14 p. (2023). Reviewer: Ana Martínez-Pastor (Valencia) MSC: 20D30 20D60 05E16 PDFBibTeX XMLCite \textit{F. Dalla Volta} and \textit{A. Lucchini}, Ars Math. Contemp. 23, No. 3, Paper No. 8, 14 p. (2023; Zbl 1515.20106) Full Text: DOI arXiv
Detomi, Eloisa; Lucchini, Andrea; Nemmi, Daniele The Engel graph of a finite group. (English) Zbl 1509.20032 Forum Math. 35, No. 1, 111-122 (2023). Reviewer: Enrico Jabara (Venezia) MSC: 20D60 05C25 PDFBibTeX XMLCite \textit{E. Detomi} et al., Forum Math. 35, No. 1, 111--122 (2023; Zbl 1509.20032) Full Text: DOI arXiv
Burness, Timothy C.; Lucchini, Andrea; Nemmi, Daniele On the soluble graph of a finite group. (English) Zbl 1517.20024 J. Comb. Theory, Ser. A 194, Article ID 105708, 39 p. (2023). Reviewer: Ramón Esteban-Romero (València) MSC: 20D10 05C25 20D05 20D60 PDFBibTeX XMLCite \textit{T. C. Burness} et al., J. Comb. Theory, Ser. A 194, Article ID 105708, 39 p. (2023; Zbl 1517.20024) Full Text: DOI arXiv
Grazian, Valentina; Lucchini, Andrea; Monetta, Carmine Group nilpotency from a graph point of view. arXiv:2303.01093 Preprint, arXiv:2303.01093 [math.GR] (2023). MSC: 20D15 05C25 BibTeX Cite \textit{V. Grazian} et al., ``Group nilpotency from a graph point of view'', Preprint, arXiv:2303.01093 [math.GR] (2023) Full Text: arXiv OA License
Lucchini, A. Minimal generating sequences of \(\mathfrak{F}\)-subgroups. (English) Zbl 07780477 J. Iran. Math. Soc. 3, No. 2, 49-60 (2022). Reviewer: Egle Bettio (Venezia) MSC: 20F05 20D60 20P05 PDFBibTeX XMLCite \textit{A. Lucchini}, J. Iran. Math. Soc. 3, No. 2, 49--60 (2022; Zbl 07780477) Full Text: DOI
Burness, Timothy C.; Garonzi, Martino; Lucchini, Andrea Finite groups, minimal bases and the intersection number. (English) Zbl 1521.20031 Trans. Lond. Math. Soc. 9, No. 1, 20-55 (2022). Reviewer: John D. Dixon (Ottawa) MSC: 20D05 20B15 20B30 20D25 PDFBibTeX XMLCite \textit{T. C. Burness} et al., Trans. Lond. Math. Soc. 9, No. 1, 20--55 (2022; Zbl 1521.20031) Full Text: DOI arXiv
Lucchini, A. Applying extremal graph theory to a question on finite groups. (English) Zbl 07644638 Acta Math. Hung. 168, No. 1, 295-299 (2022). MSC: 20D10 05C25 PDFBibTeX XMLCite \textit{A. Lucchini}, Acta Math. Hung. 168, No. 1, 295--299 (2022; Zbl 07644638) Full Text: DOI
Lucchini, Andrea; Nemmi, Daniele Forbidden subgraphs in generating graphs of finite groups. (English) Zbl 1512.20073 Algebr. Comb. 5, No. 5, 925-946 (2022). Reviewer: Mohammad-Reza Darafsheh (Tehran) MSC: 20D60 05C25 PDFBibTeX XMLCite \textit{A. Lucchini} and \textit{D. Nemmi}, Algebr. Comb. 5, No. 5, 925--946 (2022; Zbl 1512.20073) Full Text: DOI arXiv
Lucchini, Andrea A generalization of a question asked by B. H. Neumann. (English) Zbl 1514.20232 Result. Math. 77, No. 5, Paper No. 181, 5 p. (2022). Reviewer: Enric Ventura Capell (Barcelona) MSC: 20P05 20D60 PDFBibTeX XMLCite \textit{A. Lucchini}, Result. Math. 77, No. 5, Paper No. 181, 5 p. (2022; Zbl 1514.20232) Full Text: DOI arXiv
Lucchini, Andrea; Nemmi, Daniele On the connectivity of the non-generating graph. (English) Zbl 1510.20024 Arch. Math. 118, No. 6, 563-576 (2022). Reviewer: Mohammad-Reza Darafsheh (Tehran) MSC: 20D60 05C25 PDFBibTeX XMLCite \textit{A. Lucchini} and \textit{D. Nemmi}, Arch. Math. 118, No. 6, 563--576 (2022; Zbl 1510.20024) Full Text: DOI arXiv
Lucchini, Andrea; Spiga, Pablo Independent sets of generators of prime power order. (English) Zbl 1503.20003 Expo. Math. 40, No. 1, 140-154 (2022). Reviewer: Yangming Li (Guangzhou) MSC: 20D10 20D60 20F05 PDFBibTeX XMLCite \textit{A. Lucchini} and \textit{P. Spiga}, Expo. Math. 40, No. 1, 140--154 (2022; Zbl 1503.20003) Full Text: DOI arXiv
Lucchini, Andrea Maximal intersections in finite groups. (English) Zbl 1501.20003 Mediterr. J. Math. 19, No. 1, Paper No. 34, 15 p. (2022). Reviewer: Ramón Esteban-Romero (València) MSC: 20D30 20D10 20E28 PDFBibTeX XMLCite \textit{A. Lucchini}, Mediterr. J. Math. 19, No. 1, Paper No. 34, 15 p. (2022; Zbl 1501.20003) Full Text: DOI arXiv
Lucchini, Andrea; Nemmi, Daniele The non-\(\mathfrak{F}\) graph of a finite group. (English) Zbl 1522.05192 Math. Nachr. 294, No. 10, 1912-1921 (2021). MSC: 05C25 20D10 20D60 PDFBibTeX XMLCite \textit{A. Lucchini} and \textit{D. Nemmi}, Math. Nachr. 294, No. 10, 1912--1921 (2021; Zbl 1522.05192) Full Text: DOI arXiv
Lucchini, Andrea; Sabatini, Luca; Spiga, Pablo A subexponential bound on the cardinality of abelian quotients in finite transitive groups. (English) Zbl 1522.20018 Bull. Lond. Math. Soc. 53, No. 6, 1711-1716 (2021). MSC: 20B30 20B35 20B05 PDFBibTeX XMLCite \textit{A. Lucchini} et al., Bull. Lond. Math. Soc. 53, No. 6, 1711--1716 (2021; Zbl 1522.20018) Full Text: DOI arXiv
Lucchini, Andrea The virtually generating graph of a profinite group. (English) Zbl 07451285 Can. Math. Bull. 64, No. 4, 808-819 (2021). MSC: 20D60 20F05 05C25 PDFBibTeX XMLCite \textit{A. Lucchini}, Can. Math. Bull. 64, No. 4, 808--819 (2021; Zbl 07451285) Full Text: DOI arXiv
Lucchini, Andrea; Morigi, Marta; Moscatiello, Mariapia Primitive permutation IBIS groups. (English) Zbl 07385234 J. Comb. Theory, Ser. A 184, Article ID 105516, 17 p. (2021). MSC: 20Bxx 20Dxx 20-XX PDFBibTeX XMLCite \textit{A. Lucchini} et al., J. Comb. Theory, Ser. A 184, Article ID 105516, 17 p. (2021; Zbl 07385234) Full Text: DOI arXiv
Lucchini, Andrea Finite groups with the same join graph as a finite nilpotent group. (English) Zbl 07384197 Glasg. Math. J. 63, No. 3, 640-650 (2021). MSC: 20D60 20D30 PDFBibTeX XMLCite \textit{A. Lucchini}, Glasg. Math. J. 63, No. 3, 640--650 (2021; Zbl 07384197) Full Text: DOI arXiv
Lucchini, Andrea The genus of the subgroup graph of a finite group. (English) Zbl 1478.20017 Bull. Math. Sci. 11, No. 1, Article ID 2050010, 6 p. (2021). Reviewer: Jay J. Zimmerman (Towson) MSC: 20D30 20E15 20D60 05C25 PDFBibTeX XMLCite \textit{A. Lucchini}, Bull. Math. Sci. 11, No. 1, Article ID 2050010, 6 p. (2021; Zbl 1478.20017) Full Text: DOI arXiv
Lucchini, Andrea Recognizing a finite group from the generating properties of its subsets. (English) Zbl 1478.20020 Ann. Mat. Pura Appl. (4) 200, No. 1, 117-123 (2021). Reviewer: Alexander Bors (Linz) MSC: 20D60 20F05 PDFBibTeX XMLCite \textit{A. Lucchini}, Ann. Mat. Pura Appl. (4) 200, No. 1, 117--123 (2021; Zbl 1478.20020) Full Text: DOI
Acciarri, Cristina; Lucchini, Andrea Genus, thickness and crossing number of graphs encoding the generating properties of finite groups. (English) Zbl 1460.05047 Discrete Math. 344, No. 4, Article ID 112289, 7 p. (2021). MSC: 05C10 20D60 20F05 PDFBibTeX XMLCite \textit{C. Acciarri} and \textit{A. Lucchini}, Discrete Math. 344, No. 4, Article ID 112289, 7 p. (2021; Zbl 1460.05047) Full Text: DOI arXiv
Lucchini, Andrea; Moscatiello, Mariapia; Spiga, Pablo Bounding the maximal size of independent generating sets of finite groups. (English) Zbl 1477.20065 Proc. R. Soc. Edinb., Sect. A, Math. 151, No. 1, 133-150 (2021). Reviewer: Gernot Stroth (Halle) MSC: 20F05 20D60 20B30 20D20 PDFBibTeX XMLCite \textit{A. Lucchini} et al., Proc. R. Soc. Edinb., Sect. A, Math. 151, No. 1, 133--150 (2021; Zbl 1477.20065) Full Text: DOI arXiv
Lucchini, Andrea; Moscatiello, Mariapia Generation of finite groups and maximal subgroup growth. (English) Zbl 1482.20040 Adv. Group Theory Appl. 9, 39-49 (2020). Reviewer: Francesco G. Russo (Rondebosch) MSC: 20P05 20D60 20E18 20F05 PDFBibTeX XMLCite \textit{A. Lucchini} and \textit{M. Moscatiello}, Adv. Group Theory Appl. 9, 39--49 (2020; Zbl 1482.20040) Full Text: Link
Lucchini, Andrea; Nemmi, Daniele The diameter of the non-nilpotent graph of a finite group. (English) Zbl 1463.20042 Trans. Comb. 9, No. 2, 111-114 (2020). MSC: 20D60 05C25 05C12 PDFBibTeX XMLCite \textit{A. Lucchini} and \textit{D. Nemmi}, Trans. Comb. 9, No. 2, 111--114 (2020; Zbl 1463.20042) Full Text: DOI
Lucchini, Andrea; Moscatiello, Mariapia; Palcoux, Sebastien; Spiga, Pablo Boolean lattices in finite alternating and symmetric groups. (English) Zbl 1485.20060 Forum Math. Sigma 8, Paper No. e55, 35 p. (2020). MSC: 20D30 20B25 20B30 20B35 PDFBibTeX XMLCite \textit{A. Lucchini} et al., Forum Math. Sigma 8, Paper No. e55, 35 p. (2020; Zbl 1485.20060) Full Text: DOI arXiv
Lucchini, Andrea The independence graph of a finite group. (English) Zbl 1479.20019 Monatsh. Math. 193, No. 4, 845-856 (2020). Reviewer: Eshita Mazumdar (Kolkata) MSC: 20D60 05C25 PDFBibTeX XMLCite \textit{A. Lucchini}, Monatsh. Math. 193, No. 4, 845--856 (2020; Zbl 1479.20019) Full Text: DOI arXiv
Acciarri, Cristina; Lucchini, Andrea Graphs encoding the generating properties of a finite group. (English) Zbl 07261810 Math. Nachr. 293, No. 9, 1644-1674 (2020). Reviewer: Ramón Esteban-Romero (València) MSC: 20D60 20D10 05C25 PDFBibTeX XMLCite \textit{C. Acciarri} and \textit{A. Lucchini}, Math. Nachr. 293, No. 9, 1644--1674 (2020; Zbl 07261810) Full Text: DOI arXiv
Harper, Scott; Lucchini, Andrea Connectivity of generating graphs of nilpotent groups. (English) Zbl 1481.20111 Algebr. Comb. 3, No. 5, 1183-1195 (2020). MSC: 20F05 20D15 05C25 PDFBibTeX XMLCite \textit{S. Harper} and \textit{A. Lucchini}, Algebr. Comb. 3, No. 5, 1183--1195 (2020; Zbl 1481.20111) Full Text: DOI arXiv
Lucchini, Andrea; Moscatiello, Mariapia A probabilistic version of a theorem of László Kovács and Hyo-Seob Sim. (English) Zbl 1443.20096 Int. J. Group Theory 9, No. 1, 1-6 (2020). MSC: 20P05 20D10 20D60 PDFBibTeX XMLCite \textit{A. Lucchini} and \textit{M. Moscatiello}, Int. J. Group Theory 9, No. 1, 1--6 (2020; Zbl 1443.20096) Full Text: DOI
Lucchini, Andrea The generating graph of a profinite group. (English) Zbl 1481.20101 Arch. Math. 115, No. 4, 359-366 (2020). MSC: 20E18 20D60 05C25 20F05 PDFBibTeX XMLCite \textit{A. Lucchini}, Arch. Math. 115, No. 4, 359--366 (2020; Zbl 1481.20101) Full Text: DOI arXiv
Lucchini, Andrea Applying the Kövári-Sós-Turán theorem to a question in group theory. (English) Zbl 1481.20228 Commun. Algebra 48, No. 11, 4966-4968 (2020). MSC: 20P05 20D10 20D60 PDFBibTeX XMLCite \textit{A. Lucchini}, Commun. Algebra 48, No. 11, 4966--4968 (2020; Zbl 1481.20228) Full Text: DOI arXiv
Lucchini, Andrea; Marion, Claude; Tracey, Gareth Generating maximal subgroups of finite almost simple groups. (English) Zbl 1471.20024 Forum Math. Sigma 8, Paper No. e32, 67 p. (2020). Reviewer: Egle Bettio (Venezia) MSC: 20F05 20D05 20E28 PDFBibTeX XMLCite \textit{A. Lucchini} et al., Forum Math. Sigma 8, Paper No. e32, 67 p. (2020; Zbl 1471.20024) Full Text: DOI arXiv
Lucchini, Andrea; Moscatiello, Mariapia; Spiga, Pablo A polynomial bound for the number of maximal systems of imprimitivity of a finite transitive permutation group. (English) Zbl 1442.20017 Forum Math. 32, No. 3, 713-721 (2020). Reviewer: B. A. F. Wehrfritz (London) MSC: 20E28 20B05 20B15 20D60 PDFBibTeX XMLCite \textit{A. Lucchini} et al., Forum Math. 32, No. 3, 713--721 (2020; Zbl 1442.20017) Full Text: DOI arXiv
Lucchini, Andrea Finite groups with planar generating graph. (English) Zbl 1439.05105 Australas. J. Comb. 76, Part 1, 220-225 (2020). MSC: 05C25 05C10 20D60 PDFBibTeX XMLCite \textit{A. Lucchini}, Australas. J. Comb. 76, Part 1, 220--225 (2020; Zbl 1439.05105) Full Text: arXiv Link
Lucchini, Andrea; Tracey, Gareth Finite groups with large Chebotarev invariant. (English) Zbl 1444.20018 Isr. J. Math. 235, No. 1, 169-182 (2020). Reviewer: Enrico Jabara (Venezia) MSC: 20D60 20F05 20P05 PDFBibTeX XMLCite \textit{A. Lucchini} and \textit{G. Tracey}, Isr. J. Math. 235, No. 1, 169--182 (2020; Zbl 1444.20018) Full Text: DOI arXiv
Burness, Timothy C.; Garonzi, Martino; Lucchini, Andrea On the minimal dimension of a finite simple group. (English) Zbl 1477.20028 J. Comb. Theory, Ser. A 171, Article ID 105175, 32 p. (2020). MSC: 20D05 20E28 PDFBibTeX XMLCite \textit{T. C. Burness} et al., J. Comb. Theory, Ser. A 171, Article ID 105175, 32 p. (2020; Zbl 1477.20028) Full Text: DOI arXiv Link
Detomi, Eloisa; Lucchini, Andrea; Moscatiello, Mariapia; Spiga, Pablo; Traustason, Gunnar Groups satisfying a strong complement property. (English) Zbl 1446.20045 J. Algebra 535, 35-52 (2019). Reviewer: Egle Bettio (Venezia) MSC: 20E22 20D40 20D60 PDFBibTeX XMLCite \textit{E. Detomi} et al., J. Algebra 535, 35--52 (2019; Zbl 1446.20045) Full Text: DOI Link
Acciarri, Cristina; Lucchini, Andrea The generating graph of infinite abelian groups. (English) Zbl 1512.20101 Bull. Aust. Math. Soc. 100, No. 1, 68-75 (2019). MSC: 20F05 20K15 05C25 PDFBibTeX XMLCite \textit{C. Acciarri} and \textit{A. Lucchini}, Bull. Aust. Math. Soc. 100, No. 1, 68--75 (2019; Zbl 1512.20101) Full Text: DOI arXiv
Lucchini, Andrea; Moscatiello, Mariapia The Tarski irredundant basis theorem and the finite soluble groups. (English) Zbl 1454.20067 Math. Nachr. 292, No. 5, 1022-1031 (2019). Reviewer: Egle Bettio (Venezia) MSC: 20F05 20D10 PDFBibTeX XMLCite \textit{A. Lucchini} and \textit{M. Moscatiello}, Math. Nachr. 292, No. 5, 1022--1031 (2019; Zbl 1454.20067) Full Text: DOI
Lucchini, Andrea Detecting the prime divisors of the character degrees and the class sizes by a subgroup generated with few elements. (English) Zbl 1446.20040 Int. J. Group Theory 7, No. 1, 17-21 (2018). MSC: 20D60 20C15 20E45 20F05 PDFBibTeX XMLCite \textit{A. Lucchini}, Int. J. Group Theory 7, No. 1, 17--21 (2018; Zbl 1446.20040) Full Text: DOI
Detomi, Eloisa; Lucchini, Andrea; Morigi, Marta Invariable generation of groups of finite rank. (English) Zbl 1436.20056 Adv. Group Theory Appl. 6, 69-87 (2018). MSC: 20F05 20D60 PDFBibTeX XMLCite \textit{E. Detomi} et al., Adv. Group Theory Appl. 6, 69--87 (2018; Zbl 1436.20056) Full Text: DOI
Cameron, Peter J.; Lucchini, Andrea; Roney-Dougal, Colva M. Generating sets of finite groups. (English) Zbl 1429.20017 Trans. Am. Math. Soc. 370, No. 9, 6751-6770 (2018). Reviewer: Alexander Bors (Linz) MSC: 20D60 20D10 20D05 05C25 20B25 PDFBibTeX XMLCite \textit{P. J. Cameron} et al., Trans. Am. Math. Soc. 370, No. 9, 6751--6770 (2018; Zbl 1429.20017) Full Text: DOI arXiv Link
Lucchini, Andrea On the orders of the non-Frattini elements of a finite group. (English) Zbl 1425.20015 Arch. Math. 110, No. 5, 421-426 (2018). Reviewer: Marian Deaconescu (Safat) MSC: 20D60 05C25 PDFBibTeX XMLCite \textit{A. Lucchini}, Arch. Math. 110, No. 5, 421--426 (2018; Zbl 1425.20015) Full Text: DOI arXiv
Lucchini, Andrea; Maróti, Attila; Roney-Dougal, Colva M. On the generating graph of a simple group. (English) Zbl 1425.20010 J. Aust. Math. Soc. 103, No. 1, 91-103 (2017). Reviewer: Haoran Yu (Changchun) MSC: 20D06 20P05 05C25 20F05 PDFBibTeX XMLCite \textit{A. Lucchini} et al., J. Aust. Math. Soc. 103, No. 1, 91--103 (2017; Zbl 1425.20010) Full Text: DOI
Lucchini, Andrea The diameter of the generating graph of a finite soluble group. (English) Zbl 1426.20009 J. Algebra 492, 28-43 (2017). Reviewer: Ali Reza Moghaddamfar (Tehran) MSC: 20D10 20D60 05C25 05C12 20F05 PDFBibTeX XMLCite \textit{A. Lucchini}, J. Algebra 492, 28--43 (2017; Zbl 1426.20009) Full Text: DOI arXiv
Lucchini, Andrea Invariable generation of iterated wreath products of cyclic groups. (English) Zbl 1395.20017 Beitr. Algebra Geom. 58, No. 3, 477-482 (2017). Reviewer: B. A. F. Wehrfritz (London) MSC: 20E26 20E22 20F05 PDFBibTeX XMLCite \textit{A. Lucchini}, Beitr. Algebra Geom. 58, No. 3, 477--482 (2017; Zbl 1395.20017) Full Text: DOI Link
Lucchini, Andrea; Tracey, Gareth An upper bound on the Chebotarev invariant of a finite group. (English) Zbl 1380.20027 Isr. J. Math. 219, No. 1, 449-467 (2017). Reviewer: B. A. F. Wehrfritz (London) MSC: 20D60 20F05 20P05 20D99 PDFBibTeX XMLCite \textit{A. Lucchini} and \textit{G. Tracey}, Isr. J. Math. 219, No. 1, 449--467 (2017; Zbl 1380.20027) Full Text: DOI arXiv
Crestani, Eleonora; De Franceschi, Giovanni; Lucchini, Andrea Probability and bias in generating supersoluble groups. (English) Zbl 1387.20058 Proc. Edinb. Math. Soc., II. Ser. 59, No. 4, 899-909 (2016). Reviewer: Francesco G. Russo (Rondebosch) MSC: 20P05 20F16 20D10 20E18 20F05 PDFBibTeX XMLCite \textit{E. Crestani} et al., Proc. Edinb. Math. Soc., II. Ser. 59, No. 4, 899--909 (2016; Zbl 1387.20058) Full Text: DOI
Lucchini, Andrea The expected number of random elements to generate a finite group. (English) Zbl 1383.20041 Monatsh. Math. 181, No. 1, 123-142 (2016). Reviewer: Fiorenza Morini (Parma) MSC: 20P05 20B30 20F05 20D05 20E18 PDFBibTeX XMLCite \textit{A. Lucchini}, Monatsh. Math. 181, No. 1, 123--142 (2016; Zbl 1383.20041) Full Text: DOI Link
Di Summa, Marco; Lucchini, Andrea The swap graph of the finite soluble groups. (English) Zbl 1344.05068 J. Algebr. Comb. 44, No. 2, 447-454 (2016). MSC: 05C25 20D10 20F05 05C40 PDFBibTeX XMLCite \textit{M. Di Summa} and \textit{A. Lucchini}, J. Algebr. Comb. 44, No. 2, 447--454 (2016; Zbl 1344.05068) Full Text: DOI
Detomi, Eloisa; Lucchini, Andrea Maximal subgroups of finite soluble groups in general position. (English) Zbl 1358.20012 Ann. Mat. Pura Appl. (4) 195, No. 4, 1177-1183 (2016). Reviewer: Ana Martínez-Pastor (Valencia) MSC: 20D10 20E28 20F05 PDFBibTeX XMLCite \textit{E. Detomi} and \textit{A. Lucchini}, Ann. Mat. Pura Appl. (4) 195, No. 4, 1177--1183 (2016; Zbl 1358.20012) Full Text: DOI arXiv
Lucchini, Andrea; Garonzi, Martino Irredundant and minimal covers of finite groups. (English) Zbl 1352.20022 Commun. Algebra 44, No. 4, 1722-1727 (2016). Reviewer: János Kurdics (Nyíregyháza) MSC: 20D60 20E15 20E07 20E28 PDFBibTeX XMLCite \textit{A. Lucchini} and \textit{M. Garonzi}, Commun. Algebra 44, No. 4, 1722--1727 (2016; Zbl 1352.20022) Full Text: DOI arXiv
Crestani, Eleonora; Lucchini, Andrea Large \(p\)-groups without proper subgroups with the same derived length. (English) Zbl 1348.20020 Glasg. Math. J. 58, No. 2, 445-459 (2016). Reviewer: Yakov Berkovich (Afula) MSC: 20D15 20D30 20D60 PDFBibTeX XMLCite \textit{E. Crestani} and \textit{A. Lucchini}, Glasg. Math. J. 58, No. 2, 445--459 (2016; Zbl 1348.20020) Full Text: DOI
Detomi, Eloisa; Lucchini, Andrea Invariable generation of prosoluble groups. (English) Zbl 1345.20039 Isr. J. Math. 211, 481-491 (2016). Reviewer: Andrea Caranti (Trento) MSC: 20F05 20E18 20D10 20D60 20E26 PDFBibTeX XMLCite \textit{E. Detomi} and \textit{A. Lucchini}, Isr. J. Math. 211, 481--491 (2016; Zbl 1345.20039) Full Text: DOI arXiv
Crestani, Eleonora; Lucchini, Andrea Bias of group generators in finite and profinite groups: known results and open problems. (English) Zbl 1456.20077 Int. J. Group Theory 4, No. 2, 49-67 (2015). MSC: 20P05 20E18 20F05 20D60 PDFBibTeX XMLCite \textit{E. Crestani} and \textit{A. Lucchini}, Int. J. Group Theory 4, No. 2, 49--67 (2015; Zbl 1456.20077) Full Text: DOI
Lucchini, Andrea Finite soluble groups satisfying the swap conjecture. (English) Zbl 1341.20012 J. Algebr. Comb. 42, No. 4, 907-915 (2015). Reviewer: Ana Martínez-Pastor (Valencia) MSC: 20D10 20F05 05C25 PDFBibTeX XMLCite \textit{A. Lucchini}, J. Algebr. Comb. 42, No. 4, 907--915 (2015; Zbl 1341.20012) Full Text: DOI
Detomi, Eloisa; Lucchini, Andrea; Roney-Dougal, Colva M. Coprime invariable generation and minimal-exponent groups. (English) Zbl 1345.20040 J. Pure Appl. Algebra 219, No. 8, 3453-3465 (2015). Reviewer: Fiorenza Morini (Parma) MSC: 20F05 20D05 20D10 20D60 PDFBibTeX XMLCite \textit{E. Detomi} et al., J. Pure Appl. Algebra 219, No. 8, 3453--3465 (2015; Zbl 1345.20040) Full Text: DOI arXiv
Detomi, Eloisa; Lucchini, Andrea Invariable generation of permutation groups. (English) Zbl 1322.20004 Arch. Math. 104, No. 4, 301-309 (2015). Reviewer: John D. Dixon (Ottawa) MSC: 20B05 20F05 20B15 20D60 20E45 PDFBibTeX XMLCite \textit{E. Detomi} and \textit{A. Lucchini}, Arch. Math. 104, No. 4, 301--309 (2015; Zbl 1322.20004) Full Text: DOI arXiv Link
Detomi, Eloisa; Lucchini, Andrea Invariable generation with elements of coprime prime-power orders. (English) Zbl 1309.20067 J. Algebra 423, 683-701 (2015). Reviewer: John D. Dixon (Ottawa) MSC: 20P05 20F05 20D10 PDFBibTeX XMLCite \textit{E. Detomi} and \textit{A. Lucchini}, J. Algebra 423, 683--701 (2015; Zbl 1309.20067) Full Text: DOI arXiv
Garonzi, Martino; Lucchini, Andrea Covers and normal covers of finite groups. (English) Zbl 1310.20031 J. Algebra 422, 148-165 (2015). Reviewer: Rolf Brandl (Hof) MSC: 20E45 20D60 20D30 20D06 20B05 20E28 PDFBibTeX XMLCite \textit{M. Garonzi} and \textit{A. Lucchini}, J. Algebra 422, 148--165 (2015; Zbl 1310.20031) Full Text: DOI arXiv
Detomi, Eloisa; Lucchini, Andrea; Roney-Dougal, Colva M. On the probability of generating a monolithic group. (English) Zbl 1337.20077 J. Algebra 407, 413-433 (2014). MSC: 20P05 20D05 20F05 PDFBibTeX XMLCite \textit{E. Detomi} et al., J. Algebra 407, 413--433 (2014; Zbl 1337.20077) Full Text: DOI
Damian, E.; Lucchini, A. Profinite groups in which the probabilistic zeta function coincides with the subgroup zeta function. (English) Zbl 1326.20030 J. Algebra 402, 92-119 (2014). Reviewer: Rachel D. Camina (Cambridge) MSC: 20E18 11M41 20E07 20P05 20F05 PDFBibTeX XMLCite \textit{E. Damian} and \textit{A. Lucchini}, J. Algebra 402, 92--119 (2014; Zbl 1326.20030) Full Text: DOI
Dung, Duong H.; Lucchini, A. A finiteness condition on the coefficients of the probabilistic zeta function. (English) Zbl 1316.20030 Int. J. Group Theory 2, No. 1, 167-174 (2013). Reviewer: Rachel D. Camina (Cambridge) MSC: 20E18 20P05 11M41 20D06 20E07 PDFBibTeX XMLCite \textit{D. H. Dung} and \textit{A. Lucchini}, Int. J. Group Theory 2, No. 1, 167--174 (2013; Zbl 1316.20030) Full Text: arXiv
Lucchini, Andrea Minimal generating sets of maximal size in finite monolithic groups. (English) Zbl 1294.20043 Arch. Math. 101, No. 5, 401-410 (2013). Reviewer: Mohammad-Reza Darafsheh (Tehran) MSC: 20F05 20D60 PDFBibTeX XMLCite \textit{A. Lucchini}, Arch. Math. 101, No. 5, 401--410 (2013; Zbl 1294.20043) Full Text: DOI
Crestani, Eleonora; Lucchini, Andrea The generating graph of finite soluble groups. (English) Zbl 1300.20021 Isr. J. Math. 198, 63-74 (2013). Reviewer: Ana Martínez-Pastor (Valencia) MSC: 20D10 05C25 20F05 PDFBibTeX XMLCite \textit{E. Crestani} and \textit{A. Lucchini}, Isr. J. Math. 198, 63--74 (2013; Zbl 1300.20021) Full Text: DOI
Crestani, Eleonora; Lucchini, Andrea The graph of the generating \(d\)-tuples of a finite soluble group and the swap conjecture. (English) Zbl 1287.20024 J. Algebra 376, 79-88 (2013). Reviewer: Ana Martínez-Pastor (Valencia) MSC: 20D10 20F05 05C25 20D60 PDFBibTeX XMLCite \textit{E. Crestani} and \textit{A. Lucchini}, J. Algebra 376, 79--88 (2013; Zbl 1287.20024) Full Text: DOI Link
Lucchini, Andrea The largest size of a minimal generating set of a finite group. (English) Zbl 1311.20035 Arch. Math. 101, No. 1, 1-8 (2013). Reviewer: Benjamin Klopsch (Düsseldorf) MSC: 20F05 20D60 20D10 20D30 PDFBibTeX XMLCite \textit{A. Lucchini}, Arch. Math. 101, No. 1, 1--8 (2013; Zbl 1311.20035) Full Text: DOI
Detomi, E.; Lucchini, A. Probabilistic generation of finite groups with a unique minimal normal subgroup. (English) Zbl 1331.20079 J. Lond. Math. Soc., II. Ser. 87, No. 3, 689-706 (2013). Reviewer: Fiorenza Morini (Parma) MSC: 20P05 20F05 20D60 20D06 PDFBibTeX XMLCite \textit{E. Detomi} and \textit{A. Lucchini}, J. Lond. Math. Soc., II. Ser. 87, No. 3, 689--706 (2013; Zbl 1331.20079) Full Text: DOI
Crestani, Eleonora; Lucchini, Andrea The non-isolated vertices in the generating graph of a direct powers of simple groups. (English) Zbl 1276.20026 J. Algebr. Comb. 37, No. 2, 249-263 (2013). Reviewer: Mohammad-Reza Darafsheh (Tehran) MSC: 20D60 05C25 20F05 20D05 PDFBibTeX XMLCite \textit{E. Crestani} and \textit{A. Lucchini}, J. Algebr. Comb. 37, No. 2, 249--263 (2013; Zbl 1276.20026) Full Text: DOI
Crestani, Eleonora; Lucchini, Andrea \(d\)-wise generation of prosolvable groups. (English) Zbl 1271.20015 J. Algebra 369, 59-69 (2012). Reviewer: A. Caranti (Trento) MSC: 20D10 20E18 20F05 05C25 15A21 PDFBibTeX XMLCite \textit{E. Crestani} and \textit{A. Lucchini}, J. Algebra 369, 59--69 (2012; Zbl 1271.20015) Full Text: DOI
Lucchini, Andrea; Morigi, Marta; Shumyatsky, Pavel Boundedly generated subgroups of finite groups. (English) Zbl 1258.20026 Forum Math. 24, No. 4, 875-887 (2012). Reviewer: Enrico Jabara (Venezia) MSC: 20F05 20D60 20D20 20D10 PDFBibTeX XMLCite \textit{A. Lucchini} et al., Forum Math. 24, No. 4, 875--887 (2012; Zbl 1258.20026) Full Text: DOI
Crestani, Eleonora; Lucchini, Andrea Normal coverings of solvable groups. (English) Zbl 1255.20027 Arch. Math. 98, No. 1, 13-18 (2012). Reviewer: Adolfo Ballester-Bolinches (Burjasot) MSC: 20D60 20D10 PDFBibTeX XMLCite \textit{E. Crestani} and \textit{A. Lucchini}, Arch. Math. 98, No. 1, 13--18 (2012; Zbl 1255.20027) Full Text: DOI
Crestani, Eleonora; Lucchini, Andrea The generating graph of some monolithic groups. (English) Zbl 1332.20033 J. Comb. Theory, Ser. A 119, No. 3, 615-626 (2012). Reviewer: Fiorenza Morini (Parma) MSC: 20F05 05C25 20E22 20D60 20D05 05C45 PDFBibTeX XMLCite \textit{E. Crestani} and \textit{A. Lucchini}, J. Comb. Theory, Ser. A 119, No. 3, 615--626 (2012; Zbl 1332.20033) Full Text: DOI
Lucchini, Andrea Closed normal subgroups of free pro-\(S\)-groups of finite rank. (English) Zbl 1251.20029 J. Group Theory 14, No. 6, 819-823 (2011). Reviewer: Benjamin Klopsch (Egham) MSC: 20E18 20D05 20E07 20F05 PDFBibTeX XMLCite \textit{A. Lucchini}, J. Group Theory 14, No. 6, 819--823 (2011; Zbl 1251.20029) Full Text: DOI
Lucchini, Andrea; Morigi, Marta Recognizing the prime divisors of the index of a proper subgroup. (English) Zbl 1254.20022 J. Algebra 337, No. 1, 335-344 (2011). Reviewer: Evgenii I. Khukhro (Nottingham) MSC: 20D60 20D20 20F05 PDFBibTeX XMLCite \textit{A. Lucchini} and \textit{M. Morigi}, J. Algebra 337, No. 1, 335--344 (2011; Zbl 1254.20022) Full Text: DOI
Lucchini, Andrea On profinite groups with polynomially bounded Möbius numbers. (English) Zbl 1228.20026 J. Group Theory 14, No. 2, 261-271 (2011). Reviewer: A. Caranti (Trento) MSC: 20E18 20E07 20E15 20P05 20F05 11M41 PDFBibTeX XMLCite \textit{A. Lucchini}, J. Group Theory 14, No. 2, 261--271 (2011; Zbl 1228.20026) Full Text: DOI
Lucchini, Andrea Profinite groups with nonabelian crowns of bounded rank and their probabilistic zeta function. (English) Zbl 1235.20028 Isr. J. Math. 181, 53-64 (2011). Reviewer: Martyn Dixon (Tuscaloosa) MSC: 20E18 20E07 20E15 20P05 20F05 11M41 PDFBibTeX XMLCite \textit{A. Lucchini}, Isr. J. Math. 181, 53--64 (2011; Zbl 1235.20028) Full Text: DOI
Garonzi, Martino; Lucchini, Andrea Direct products of finite groups as unions of proper subgroups. (English) Zbl 1223.20018 Arch. Math. 95, No. 3, 201-206 (2010). Reviewer: Adolfo Ballester-Bolinches (Burjasot) MSC: 20D60 20D30 PDFBibTeX XMLCite \textit{M. Garonzi} and \textit{A. Lucchini}, Arch. Math. 95, No. 3, 201--206 (2010; Zbl 1223.20018) Full Text: DOI arXiv
Lucchini, Andrea On the subgroups with non-trivial Möbius number. (English) Zbl 1206.20032 J. Group Theory 13, No. 4, 589-600 (2010). Reviewer: A. Caranti (Trento) MSC: 20E18 20E07 20E15 20P05 20F05 11M41 PDFBibTeX XMLCite \textit{A. Lucchini}, J. Group Theory 13, No. 4, 589--600 (2010; Zbl 1206.20032) Full Text: DOI
Breuer, T.; Guralnick, R. M.; Lucchini, A.; Maróti, A.; Nagy, G. P. Hamiltonian cycles in the generating graphs of finite groups. (English) Zbl 1223.20058 Bull. Lond. Math. Soc. 42, No. 4, 621-633 (2010). Reviewer: Fiorenza Morini (Parma) MSC: 20P05 20D60 20F05 05C45 05C25 20D06 PDFBibTeX XMLCite \textit{T. Breuer} et al., Bull. Lond. Math. Soc. 42, No. 4, 621--633 (2010; Zbl 1223.20058) Full Text: DOI
Lucchini, Andrea; Maróti, Attila On finite simple groups and Kneser graphs. (English) Zbl 1206.20024 J. Algebr. Comb. 30, No. 4, 549-566 (2009). Reviewer: Anatoli Kondrat’ev (Ekaterinburg) MSC: 20D60 20D06 05C25 05C15 20F05 20G40 PDFBibTeX XMLCite \textit{A. Lucchini} and \textit{A. Maróti}, J. Algebr. Comb. 30, No. 4, 549--566 (2009; Zbl 1206.20024) Full Text: DOI
Lucchini, Andrea; Maróti, Attila Some results and questions related to the generating graph a finite group. (English) Zbl 1191.20018 Bianchi, Mariagrazia (ed.) et al., Ischia group theory 2008. Proceedings of the conference in group theory, Naples, Italy, April 1–4, 2008. Hackensack, NJ: World Scientific (ISBN 978-981-4277-79-2/pbk). 183-208 (2009). Reviewer: Alireza Abdollahi (Isfahan) MSC: 20D60 05C25 20F05 20D30 20D05 20E45 16P20 16U60 PDFBibTeX XMLCite \textit{A. Lucchini} and \textit{A. Maróti}, in: Ischia group theory 2008. Proceedings of the conference in group theory, Naples, Italy, April 1--4, 2008. Hackensack, NJ: World Scientific. 183--208 (2009; Zbl 1191.20018)
Lucchini, Andrea; Maróti, Attila On the clique number of the generating graph of a finite group. (English) Zbl 1179.05052 Proc. Am. Math. Soc. 137, No. 10, 3207-3217 (2009). MSC: 05C25 20D10 20P05 PDFBibTeX XMLCite \textit{A. Lucchini} and \textit{A. Maróti}, Proc. Am. Math. Soc. 137, No. 10, 3207--3217 (2009; Zbl 1179.05052) Full Text: DOI
Lucchini, Andrea; Massa, Marilena The probabilistic zeta function of alternating and symmetric groups. (English) Zbl 1189.20018 Algebra Colloq. 16, No. 2, 195-210 (2009). Reviewer: Anatoli Kondrat’ev (Ekaterinburg) MSC: 20D06 20P05 11M41 20B35 20D60 20D30 PDFBibTeX XMLCite \textit{A. Lucchini} and \textit{M. Massa}, Algebra Colloq. 16, No. 2, 195--210 (2009; Zbl 1189.20018) Full Text: DOI
Lucchini, Andrea; Tamburini, M. Chiara Nilpotent groups of semilinear transformations which are monomial. (English) Zbl 1225.20018 Matematiche 63, No. 2, 3-18 (2008). Reviewer: Nan Ji-Zhu (Dalian) MSC: 20D15 20G40 20D20 20D25 PDFBibTeX XMLCite \textit{A. Lucchini} and \textit{M. C. Tamburini}, Matematiche 63, No. 2, 3--18 (2008; Zbl 1225.20018) Full Text: Link
Detomi, Eloisa; Lucchini, Andrea On the structure of primitive \(n\)-sum groups. (English) Zbl 1163.20015 Cubo 10, No. 3, 195-210 (2008). Reviewer: John D. Dixon (Ottawa) MSC: 20D60 20D30 PDFBibTeX XMLCite \textit{E. Detomi} and \textit{A. Lucchini}, Cubo 10, No. 3, 195--210 (2008; Zbl 1163.20015)
Lucchini, Andrea; Menegazzo, Federico; Morigi, Marta Complements of the socle in monolithic groups. (English) Zbl 1162.20012 Groups Geom. Dyn. 1, No. 4, 585-611 (2007). Reviewer: John D. Dixon (Ottawa) MSC: 20D40 20E45 20D60 20D05 20D30 20J06 PDFBibTeX XMLCite \textit{A. Lucchini} et al., Groups Geom. Dyn. 1, No. 4, 585--611 (2007; Zbl 1162.20012) Full Text: DOI
Damian, E.; Lucchini, A. Finite groups with \(p\)-multiplicative probabilistic zeta function. (English) Zbl 1149.20022 Commun. Algebra 35, No. 11, 3451-3472 (2007). Reviewer: John D. Dixon (Ottawa) MSC: 20D60 20D30 11M41 20D06 PDFBibTeX XMLCite \textit{E. Damian} and \textit{A. Lucchini}, Commun. Algebra 35, No. 11, 3451--3472 (2007; Zbl 1149.20022) Full Text: DOI
Lucchini, Andrea Subgroups of solvable groups with non-zero Möbius function. (English) Zbl 1130.20027 J. Group Theory 10, No. 5, 633-639 (2007). Reviewer: John D. Dixon (Ottawa) MSC: 20E18 20E07 20D10 20D30 11M41 20P05 20F05 PDFBibTeX XMLCite \textit{A. Lucchini}, J. Group Theory 10, No. 5, 633--639 (2007; Zbl 1130.20027) Full Text: DOI
Detomi, Eloisa; Lucchini, Andrea Non-prosoluble profinite groups with a rational probabilistic zeta function. (English) Zbl 1138.20028 J. Group Theory 10, No. 4, 453-466 (2007). Reviewer: Benjamin Klopsch (Egham) MSC: 20E18 11M41 20E07 20F14 PDFBibTeX XMLCite \textit{E. Detomi} and \textit{A. Lucchini}, J. Group Theory 10, No. 4, 453--466 (2007; Zbl 1138.20028) Full Text: DOI
Damian, Erika; Lucchini, Andrea The probabilistic zeta function of finite simple groups. (English) Zbl 1127.20052 J. Algebra 313, No. 2, 957-971 (2007). Reviewer: Mohammad-Reza Darafsheh (Tehran) MSC: 20P05 11M41 20D30 20D06 20D25 20E28 20D08 PDFBibTeX XMLCite \textit{E. Damian} and \textit{A. Lucchini}, J. Algebra 313, No. 2, 957--971 (2007; Zbl 1127.20052) Full Text: DOI
Damian, Erika; Lucchini, Andrea On the Dirichlet polynomial of finite groups of Lie type. (English) Zbl 1167.20334 Rend. Semin. Mat. Univ. Padova 115, 51-69 (2006). MSC: 20P05 11M41 20D30 20D06 PDFBibTeX XMLCite \textit{E. Damian} and \textit{A. Lucchini}, Rend. Semin. Mat. Univ. Padova 115, 51--69 (2006; Zbl 1167.20334) Full Text: EuDML Link
Lucchini, Andrea; Menegazzo, Federico; Morigi, Marta On the probability of generating prosoluble groups. (English) Zbl 1158.20010 Isr. J. Math. 155, 93-115 (2006). Reviewer: Benjamin Klopsch (Egham) MSC: 20E07 20D10 20E18 20F05 20E28 20P05 PDFBibTeX XMLCite \textit{A. Lucchini} et al., Isr. J. Math. 155, 93--115 (2006; Zbl 1158.20010) Full Text: DOI
Detomi, Eloisa; Lucchini, Andrea Profinite groups with a rational probabilistic zeta function. (English) Zbl 1111.20031 J. Group Theory 9, No. 2, 203-217 (2006). Reviewer: John D. Dixon (Ottawa) MSC: 20E18 11M41 20E07 20P05 PDFBibTeX XMLCite \textit{E. Detomi} and \textit{A. Lucchini}, J. Group Theory 9, No. 2, 203--217 (2006; Zbl 1111.20031) Full Text: DOI