Pairwise generating and covering sporadic simple groups.

DOI10.1016/j.jalgebra.2009.10.011zbMath1202.20019OpenAlexW2056994767MaRDI QIDQ984990

Attila Maróti, Petra E. Holmes

Publication date: 20 July 2010

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jalgebra.2009.10.011

zbMATH Keywords

sporadic simple groupsgraphsgenerationsubgroup coveringspairwise generating sets

Mathematics Subject Classification ID

Simple groups: sporadic groups (20D08) Arithmetic and combinatorial problems involving abstract finite groups (20D60) Series and lattices of subgroups (20D30) Generators, relations, and presentations of groups (20F05)

Related Items

On the covering number of symmetric groups having degree divisible by six. ⋮ On the covering number of \(S_{14}\) ⋮ On the covering number of small symmetric groups and some sporadic simple groups. ⋮ On Integers that are Covering Numbers of Groups ⋮ The non-isolated vertices in the generating graph of a direct powers of simple groups. ⋮ Covering the set of \(p\)-elements in finite groups by Sylow \(p\)-subgroups ⋮ Covers and normal covers of finite groups. ⋮ The solvability of groups with nilpotent minimal coverings.

Uses Software

• GAP
• Magma

Cites Work

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• Sets of permutations that generate the symmetric group pairwise.
• The probability of generating a finite simple group
• Simple groups, probabilistic methods, and a conjecture of Kantor and Lubotzky
• Sets of elements that pairwise generate a linear group
• Subgroup coverings of some sporadic groups.
• The probability of generating a finite classical group
• Groups as the union of proper subgroups.
• On $n$-Sum Groups.
• Groups Covered By Permutable Subsets
• The probability of generating the symmetric group

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