18 November 2018
Bulletin of the London Mathematical Society
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.
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