Profinite extensions of centralizers and the profinite completion of limit groups

TL;DR

This paper introduces a new class of profinite groups formed by extensions of centralizers, explores their structure and homological properties, and connects them to the profinite completions of limit groups, advancing understanding in group theory.

Contribution

It defines and studies a novel class of profinite groups related to limit groups, providing new insights into their structure and homological characteristics.

Findings

Profinite completions of limit groups belong to this new class.

Results on the group-theoretical structure of these profinite groups.

Analysis of their homological properties.

Abstract

We introduce and investigate a class of profinite groups defined via extensions of centralizers analogous to the extensively studied class of finitely generated fully residually free groups, that is, limit groups (in the sense of Z. Sela). From the fact that the profinite completion of limit groups belong to this class, results on their group-theoretical structure and homological properties are obtained.