Generators and relations for wreath products

TL;DR

This paper provides a presentation of wreath products of groups through generators and relations, highlighting minimality conditions and specific cases like Sylow subgroups of symmetric groups.

Contribution

It introduces a method to derive minimal generators and relations for wreath products, including special cases such as Sylow subgroups.

Findings

Generators and relations for wreath products are explicitly given.

Minimal presentations are achieved under certain conditions.

Sylow subgroups of symmetric groups are examples of minimal cases.

Abstract

Generators and defining relations for wreath products of groups are given. Under some condition (conormality of the generators) they are minimal. In particular, it is just the case for the Sylow subgroups of the symmetric groups.