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arXiv · 2301.03691

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

Martino Garonzi·Julia Almeida
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Abstract

The covering number of a finite group $G$, denoted $\sigma(G)$, is the smallest positive integer $k$ such that $G$ is a union of $k$ proper subgroups. We calculate $\sigma(G)$ 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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Martino Garonzi, Julia Almeida. 2023-01-09. On minimal coverings and pairwise generation of some primitive groups of wreath product type. https://arxiv.org/abs/2301.03691

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