On minimal coverings and pairwise generation of some primitive groups of wreath product type

2023/01/09 by Martino Garonzi, Garonzi, Martino, Julia Sousa Martins de Almeida +1 · 1 citation
Mathematics · #Finite Group Theory Research #Limits and Structures in Graph Theory

paper · pdf · doi:10.48550/arxiv.2301.03691

Abstract

The covering number of a finite group G, denoted σ(G), is the smallest positive integer k such that G is a union of k proper subgroups. We calculate σ(G) for a family of primitive groups G with a unique minimal normal subgroup N, isomorphic to A_n^m with n divisible by 6 and G/N cyclic. This is a generalization of a result of E. Swartz concerning the symmetric groups. We also prove an asymptotic result concerning pairwise generation.

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• Covering the set of p-elements in finite groups by Sylow p-subgroups

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