Weak commutativity and finiteness properties of groups

Author: 

Bridson, M
Kochloukova, D

Publication Date: 

18 November 2018

Journal: 

Bulletin of the London Mathematical Society

Last Updated: 

2020-07-04T04:35:07.82+01:00

Issue: 

1

Volume: 

51

DOI: 

10.1112/blms.12219

page: 

168-180

abstract: 

We consider the groupX(G) obtained fromG∗Gby forcing each elementgin the first freefactor to commute with the copy ofgin the second free factor. Deceptively complicated finitelypresented groups arise from this construction:X(G) is finitely presented if and only ifGis finitelypresented, but ifFis a non-abelian free group of finite rank thenX(F) has a subgroup of finiteindex whose third homology is not finitely generated.

Symplectic id: 

702608

Submitted to ORA: 

Submitted

Publication Type: 

Journal Article