Linear bounds for the normal covering number of the symmetric and alternating groups

Abstract

The normal covering number $\gamma (G)$ of a finite, non-cyclic group $G$ is the minimum number of proper subgroups such that each element of $G$ lies in some conjugate of one of these subgroups. We find lower bounds linear in $n$ for $\gamma (S_n)$, when $n$ is even, and for $\gamma (A_n)$, when $n$ is odd.

Cited by in corpus (1)

• Normal covering numbers for $S_n$ and $A_n$ and additive combinatorics