Characterization of layer-finite groups in the class of periodic groups (Q1081699)
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scientific article; zbMATH DE number 3971043
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Characterization of layer-finite groups in the class of periodic groups |
scientific article; zbMATH DE number 3971043 |
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Characterization of layer-finite groups in the class of periodic groups (English)
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1985
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The group G is called conjugately biprimitively finite if, for any finite subgroup H, any two conjugate elements of prime order in \(N_ G(H)/H\) generate a finite subgroup. A group in which the set of elements of each order is finite is called layer-finite. Theorem: Let G be a periodic group with all its finite subgroups soluble. If G is conjugately biprimitively finite and all its locally finite subgroups are layer- finite, then G is layer-finite.
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conjugately biprimitively finite groups
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layer-finite groups
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periodic group
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locally finite subgroups
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