Quotients of permutation groups by nonabelian minimal normal subgroups

TL;DR

This paper proves that quotients of permutation groups by nonabelian minimal normal subgroups embed into smaller symmetric groups, with improved bounds for transitive groups, extending previous results in group theory.

Contribution

The paper provides a new embedding result for such quotients and improves bounds specifically for transitive permutation groups.

Findings

Quotients embed into Sym(m) with m<n

For transitive groups, m ≤ 2n/5

Extends and refines previous embedding results

Abstract

We prove that a quotient G/N of a subgroup G of Sym(n) by a nonabelian minimal normal subgroup N of G embeds into Sym(m) for some $m<n$. This result was proved previously by Robert Chamberlain, and we also prove that,if G is transitive, then we can take m \le 2n/5.