On the maximal number of elements pairwise generating the symmetric group of even degree

DOI10.1016/j.disc.2021.112776zbMath1491.20060arXiv2011.14426OpenAlexW4206630172MaRDI QIDQ2075524

Attila Maróti, Martino Garonzi, Francesco Fumagalli

Publication date: 14 February 2022

Published in: Discrete Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2011.14426

zbMATH Keywords

coveringsymmetric groupLovász local lemmagroup generation

Mathematics Subject Classification ID

Arithmetic and combinatorial problems involving abstract finite groups (20D60) Generators, relations, and presentations of groups (20F05) Symmetric groups (20B30) Combinatorial aspects of groups and algebras (05E16)

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Cites Work

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• On the covering number of small symmetric groups and some sporadic simple groups.
• Sets of permutations that generate the symmetric group pairwise.
• On the covering number of \(S_{14}\)
• Covering the symmetric groups with proper subgroups.
• Simple groups, probabilistic methods, and a conjecture of Kantor and Lubotzky
• Maximal subgroups of symmetric groups
• Sets of elements that pairwise generate a linear group
• The symmetric group of degree six can be covered by 13 and no fewer proper subgroups.
• On the covering number of symmetric groups having degree divisible by six.
• On the clique number of the generating graph of a finite group
• On the orders of Primitive Permutation Groups
• Groups as the union of proper subgroups.
• On $n$-Sum Groups.
• The probability of generating the symmetric group