Centralisers of Finite Subgroups in Soluble Groups of Type FP_n

TL;DR

This paper investigates the properties of centralisers of finite subgroups within soluble groups of type FPn, revealing that such centralisers may not necessarily share the same finiteness property.

Contribution

It demonstrates that in soluble groups of type FPn, centralisers of finite subgroups can fail to be of type FPn, challenging assumptions about subgroup properties.

Findings

Centralisers of finite subgroups in soluble groups of type FPn may not be of type FPn.

The paper provides examples or proofs showing the failure of this property.

It advances understanding of subgroup structures in soluble groups.

Abstract

We show that for soluble groups of type FPn, centralisers of finite subgroups need not be of type FPn.