Sets of permutations that generate the symmetric group pairwise.

DOI10.1016/j.jcta.2006.01.001zbMath1104.20001OpenAlexW2061522109MaRDI QIDQ855853

Simon R. Blackburn

Publication date: 7 December 2006

Published in: Journal of Combinatorial Theory. Series A (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jcta.2006.01.001

zbMATH Keywords

symmetric groupsalternating groupsgenerating permutationssubgroup coverings

Mathematics Subject Classification ID

Permutations, words, matrices (05A05) Generators, relations, and presentations of groups (20F05) Symmetric groups (20B30)

Related Items (18)

On the covering number of symmetric groups having degree divisible by six. ⋮ On the covering number of \(S_{14}\) ⋮ On the clique number of the generating graph of a finite group ⋮ On the covering number of small symmetric groups and some sporadic simple groups. ⋮ On the generating graph of direct powers of a simple group. ⋮ On Integers that are Covering Numbers of Groups ⋮ The non-isolated vertices in the generating graph of a direct powers of simple groups. ⋮ On the maximal number of elements pairwise generating the finite alternating group ⋮ Sets of elements that pairwise generate a linear group ⋮ The independence graph of a finite group ⋮ Normal coverings and pairwise generation of finite alternating and symmetric groups. ⋮ Covers and normal covers of finite groups. ⋮ Normal coverings of solvable groups. ⋮ On finite simple groups and Kneser graphs. ⋮ Pairwise generating and covering sporadic simple groups. ⋮ d-WISE GENERATION OF SOME INFINITE GROUPS ⋮ On the maximal number of elements pairwise generating the symmetric group of even degree ⋮ Improved Bounds for the Spread of Sporadic Groups

Cites Work

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• Minimal covers of \(S_ n\) by abelian subgroups and maximal subsets of pairwise noncommuting elements. II
• On a problem of Spencer
• Minimal covers of \(S_ n\) by Abelian subgroups and maximal subsets of pairwise noncommuting elements
• Covering the symmetric groups with proper subgroups.
• Maximal subgroups of symmetric groups
• Groups as Unions of Proper Subgroups
• On the orders of Primitive Permutation Groups
• On $n$-Sum Groups.
• Groups Which are the Union of Three Subgroups

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