Covering certain Wreath Products with Proper Subgroups

TL;DR

This paper investigates the minimal number of proper subgroups needed to cover certain wreath products involving nonabelian finite simple groups and cyclic groups, providing formulas and estimates.

Contribution

It offers new formulas and estimates for the covering number of wreath products of nonabelian finite simple groups with cyclic groups.

Findings

Derived formulas for (S \u2297 C_m) for specific simple groups S.

Provided bounds and estimates for the covering number (S \u2297 C_m).

Enhanced understanding of subgroup coverings in complex group structures.

Abstract

For a non-cyclic finite group $X$ let $\sigma(X)$ be the least number of proper subgroups of $X$ whose union is $X$. Precise formulas or estimates are given for $\sigma(S \wr C_{m})$ for certain nonabelian finite simple groups $S$ where $C_m$ is a cyclic group of order $m$.