Generating wreath products of symmetric and alternating groups

TL;DR

This paper proves that the wreath product of two finite symmetric or alternating groups can be generated by just two elements, simplifying understanding of their algebraic structure.

Contribution

It establishes that the wreath product of two finite symmetric or alternating groups is 2-generated, a new result in group theory.

Findings

Wreath products of symmetric groups are 2-generated.

Wreath products of alternating groups are 2-generated.

Simplifies the understanding of the structure of these groups.

Abstract

We show that the wreath product of two finite symmetric or alternating groups is 2-generated.