Constructing representations of finite groups and applications to finitely presented groups (Q1265516)
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scientific article; zbMATH DE number 1203878
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Constructing representations of finite groups and applications to finitely presented groups |
scientific article; zbMATH DE number 1203878 |
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Constructing representations of finite groups and applications to finitely presented groups (English)
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18 October 1999
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The group \(G^{3,7,n}\) is defined by the presentation \[ \langle x,y,z\mid x^2, y^2, z^2, (xy)^2, (xz)^3, (yz)^7, (xyz)^n\rangle. \] It is a famous problem whether the group \(G^{3,7,23}\) is infinite or not. Here is a very elegant proof that \(G^{3,7,23}\) is infinite by exploiting the representation theory of a finite factor group. The method is described in detail and applicable in a more general context.
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representations of groups
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finitely presented groups
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presentations
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finite factor groups
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