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...
| প্রধান লেখক: | , |
|---|---|
| বিন্যাস: | Journal article |
| প্রকাশিত: |
London Mathematical Society
2018
|
| সংক্ষিপ্ত: | 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. |
|---|