Covering certain Wreath Products with Proper Subgroups

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 $m$.