The homology of groups, profinite completions, and echoes of Gilbert Baumslag

Author: 

Bridson, M

Publication Date: 

10 February 2020

Journal: 

Elementary Theory of Groups and Group Rings, and Related topics

Last Updated: 

2021-08-23T08:41:33.133+01:00

DOI: 

10.1515/9783110638387-003

page: 

11-28

abstract: 

We present novel constructions concerning the homology of finitely generated groups. Each construction draws on ideas of Gilbert Baumslag. There is a finitely presented acyclic group U such that U has no proper subgroups of finite index and every finitely presented group can be embedded in U. There is no algorithm that can determine whether or not a finitely presentable subgroup of a residually finite, biautomatic group is perfect. For every recursively presented abelian group A, there exists a pair of groups i : PA → GA such that i induces an isomorphism of profinite completions, where GA is a torsion-free biautomatic group that is residually finite and superperfect, while PA is a finitely generated group with H2(PA,ℤ) ≅ A.

Symplectic id: 

1055459

Submitted to ORA: 

Submitted

Publication Type: 

Journal Article

ISBN-13: 

978-3-11-063673-4