On the undecidability of some classes of abelian-by-finite groups (Q688804)
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scientific article; zbMATH DE number 438521
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the undecidability of some classes of abelian-by-finite groups |
scientific article; zbMATH DE number 438521 |
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On the undecidability of some classes of abelian-by-finite groups (English)
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30 November 1993
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For any group \(G\) and every formula \(\varphi(v)\) in the first-order language of groups, \(K(G,\varphi)\) denote the class of groups \(H\) such that \(\varphi(H)\) is a normal Abelian subgroup of \(H\) and \(H/\varphi(H)\cong G\). The main result is the following theorem: Let \(G\) be a finite nilpotent group whose order is not square-free. Then there is a formula \(\varphi(v)\) such that the theory of \(K(G,\varphi)\) is undecidable.
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Abelian-by-finite groups
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undecidability
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finite nilpotent group
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