Generalization of Hamiltonian groups (Q684361)
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scientific article; zbMATH DE number 411639
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Generalization of Hamiltonian groups |
scientific article; zbMATH DE number 411639 |
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Generalization of Hamiltonian groups (English)
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13 September 1993
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The following properties are considered: (CO) the core of every subgroup \(H\) of \(G\) is the irredundant intersection of the distinct conjugates of \(H\) and (NC) the normal closure of every subgroup of \(H\) is irredundantly generated by the distinct conjugates of \(H\). It is shown that each of these properties is equivalent to every subgroup of \(G\) having at most 2 conjugates. Such groups are nilpotent and centre-by-finite.
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\(FC\)-group
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centre-by-finite group
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core
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subgroup
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irredundant intersection
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normal closure
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nilpotent
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