Finiteness properties of profinite groups

TL;DR

This paper explores the relationships between various finiteness properties of profinite groups, which are compact topological groups linked to finite groups, and examines their implications for the structure of finite and profinite groups.

Contribution

It provides new insights into how different finiteness properties of profinite groups relate and influence their structural characteristics.

Findings

Identifies key relationships between finiteness properties in profinite groups

Shows implications of these properties for the structure of finite groups

Advances understanding of the interplay between topological and algebraic aspects

Abstract

Broadly speaking, a finiteness property of groups is any generalisation of the property of having finite order. A large part of infinite group theory is concerned with finiteness properties and the relationships between them. Profinite groups are an important case of this, being compact topological groups that possess an intimate connection with their finite images. This thesis investigates the relationship between several finiteness properties that a profinite group may have, with consequences for the structure of finite and profinite groups.