On the covering number of symmetric groups having degree divisible by six.

DOI10.1016/j.disc.2016.05.004zbMath1344.20036arXiv1410.7524OpenAlexW2419500219MaRDI QIDQ2629265

Eric Swartz

Publication date: 5 July 2016

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

Full work available at URL: https://arxiv.org/abs/1410.7524

zbMATH Keywords

symmetric groupsnumbers of subgroupsunions of subgroupscovering numberscovers of groups

Mathematics Subject Classification ID

Arithmetic and combinatorial problems involving abstract finite groups (20D60) Series and lattices of subgroups (20D30) Symmetric groups (20B30)

Related Items (12)

On the covering number of \(S_{14}\) ⋮ On the covering number of small symmetric groups and some sporadic simple groups. ⋮ Covering modules by proper submodules ⋮ On Integers that are Covering Numbers of Groups ⋮ Covering the set of \(p\)-elements in finite groups by Sylow \(p\)-subgroups ⋮ On the maximal number of elements pairwise generating the finite alternating group ⋮ The covering numbers of rings ⋮ A new infinite family of σ -elementary rings ⋮ On the primary coverings of finite solvable and symmetric groups ⋮ Maximal Subrings and Covering Numbers of Finite Semisimple Rings ⋮ On groups covered by finitely many centralizers and domination number of the commuting graphs ⋮ On the maximal number of elements pairwise generating the symmetric group of even degree

Uses Software

• GAP

Cites Work

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• On the covering number of small symmetric groups and some sporadic simple groups.
• Covers and normal covers of finite groups.
• Normal coverings of finite symmetric and alternating groups.
• Rings as the unions of proper subrings.
• Direct products of finite groups as unions of proper subgroups.
• Sets of permutations that generate the symmetric group pairwise.
• Pairwise generating and covering sporadic simple groups.
• Covering the symmetric groups with proper subgroups.
• On the orders of primitive groups
• Sets of elements that pairwise generate a linear group
• Corrigendum to ``Sets of elements that pairwise generate a linear group [J. Comb. Theory, Ser. A 115, No.\,3, 442--465 (2008)]
• Normal coverings of linear groups.
• Normal coverings and pairwise generation of finite alternating and symmetric groups.
• The symmetric group of degree six can be covered by 13 and no fewer proper subgroups.
• Subgroup coverings of some sporadic groups.
• On loops covered by subloops.
• Irredundant and Minimal Covers of Finite Groups
• Covering certain wreath products with proper subgroups
• Groups as Unions of Proper Subgroups
• Covering Numbers of Finite Rings
• Groups as the union of proper subgroups.
• Subgroup coverings of some linear groups
• On $n$-Sum Groups.
• Covering Certain Monolithic Groups with Proper Subgroups
• FINITE GROUPS THAT ARE THE UNION OF AT MOST 25 PROPER SUBGROUPS
• Covering monolithic groups with proper subgroups
• Conjectures on the normal covering number of the finite symmetric and alternating groups
• Groups Covered By Permutable Subsets

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