Characterization of groups with layer-finite periodic part (Q2754826)
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scientific article; zbMATH DE number 1668447
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Characterization of groups with layer-finite periodic part |
scientific article; zbMATH DE number 1668447 |
Statements
4 November 2001
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layer-finite groups
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solvable subgroups
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periodic part
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locally finite groups
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Shunkov groups
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Characterization of groups with layer-finite periodic part (English)
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A group is called layer-finite if every set of elements of the same order is finite (such groups were studied by S. N. Chernikov). The main theorem of the paper states that a Shunkov group with solvable finite subgroups has layer-finite periodic part if and only if its periodic locally solvable subgroups are layer-finite (a group \(G\) is called a Shunkov group if for any finite subgroup \(H\subseteq G\) every two conjugate elements in the factor-group \(N_G(H)/H\) generate a finite subgroup).
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