Group algebras with every proper quotient finite dimensional (Q1109854)
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scientific article; zbMATH DE number 4071124
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Group algebras with every proper quotient finite dimensional |
scientific article; zbMATH DE number 4071124 |
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Group algebras with every proper quotient finite dimensional (English)
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1988
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The following result is proved. Let K be a field and let G be an infinite group containing either a nontrivial normal abelian subgroup or a nontrivial finite normal subgroup. Then K[G]/I is finite dimensional over K for all nonzero ideals I of the group algebra K[G] if and only if G is either infinite cyclic or infinite dihedral.
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normal abelian subgroup
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finite dimensional
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group algebra
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infinite cyclic
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infinite dihedral
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