Normal coverings of finite symmetric and alternating groups.

DOI10.1016/j.jcta.2011.03.008zbMath1248.20005arXiv1011.4368OpenAlexW2011889037WikidataQ56987633 ScholiaQ56987633MaRDI QIDQ549247

Daniela Bubboloni, Cheryl E. Praeger

Publication date: 7 July 2011

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

Full work available at URL: https://arxiv.org/abs/1011.4368

zbMATH Keywords

conjugacy classessymmetric groupsalternating groupscoverings of groups

Mathematics Subject Classification ID

Conjugacy classes for groups (20E45) Arithmetic and combinatorial problems involving abstract finite groups (20D60) Arithmetic functions; related numbers; inversion formulas (11A25) Symmetric groups (20B30) Subgroups of symmetric groups (20B35)

Related Items

Primitive permutation groups and derangements of prime power order. ⋮ On the covering number of symmetric groups having degree divisible by six. ⋮ Covering a semi-direct product and intersective polynomials ⋮ 2-coverings for exceptional and sporadic simple groups. ⋮ Coprime partitions and Jordan totient functions ⋮ Affine transformations of finite vector spaces with large orders or few cycles. ⋮ Nilpotent covers of symmetric and alternating groups ⋮ Conjugacy classes of maximal cyclic subgroups ⋮ Normal coverings and pairwise generation of finite alternating and symmetric groups. ⋮ Compositions of n satisfying some coprimality conditions ⋮ Covers and normal covers of finite groups. ⋮ Normal coverings of solvable groups. ⋮ PRIMITIVE PERMUTATION GROUPS CONTAINING A CYCLE ⋮ Intersective \(S_n\) polynomials with few irreducible factors ⋮ Linear bounds for the normal covering number of the symmetric and alternating groups ⋮ On groups covered by finitely many centralizers and domination number of the commuting graphs ⋮ On the indices of maximal subgroups and the normal primary coverings of finite groups ⋮ Finite primitive permutation groups containing a permutation having at most four cycles

Uses Software

• ATLAS Group Representations

Cites Work

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• Cyclic regular subgroups of primitive permutation groups
• On $n$-Sum Groups.
• Polynomials with roots modulo every integer
• On Galois Realizations of the 2-Coverable Symmetric and Alternating Groups

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