Residual finiteness and Hopficity of certain HNN extensions (Q1066269)
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scientific article; zbMATH DE number 3925083
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Residual finiteness and Hopficity of certain HNN extensions |
scientific article; zbMATH DE number 3925083 |
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Residual finiteness and Hopficity of certain HNN extensions (English)
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1986
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Let \(G=<t,K|\) \(t^{-1}At=B,\phi >\) be an HNN extension, where K is a finitely generated abelian group. A necessary and sufficient condition is given for the group G to be residually finite in the case where A, B are of finite index in K. If K is free abelian of rank 2 and A and B are infinite cyclic then a complete characterization is given with respect to residual finiteness and hopficity.
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HNN extension
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finitely generated abelian group
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residually finite
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hopficity
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