Groups with systems of invariant subgroups of infinite index (Q1080948)
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scientific article; zbMATH DE number 3968888
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Groups with systems of invariant subgroups of infinite index |
scientific article; zbMATH DE number 3968888 |
Statements
Groups with systems of invariant subgroups of infinite index (English)
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1986
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Let G be a non-periodic group in which any subgroup of infinite index is normal. Then G is a semidirect product of a Hamiltonian group H and an infinite cyclic group C. Conversely, let G be a semidirect product of H and C. If any cyclic subgroup in H is normal in G then any subgroup of infinite index is normal in G.
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non-periodic group
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subgroup of infinite index
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semidirect product
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Hamiltonian group
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infinite cyclic group
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