Weak commutativity and finiteness properties of groups
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 n...
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| Format: | Journal article |
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London Mathematical Society
2018
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| Summary: | 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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