On locally finite groups with a Chernikov maximal subgroup

Name: On locally finite groups with a Chernikov maximal subgroup
Creator: Hartley, B.
Keywords: Extensions, wreath products, and other compositions of groups, Maximal subgroups, Periodic groups; locally finite groups, Subgroup theorems; subgroup growth, 0102 computer and information sciences, 0101 mathematics, Chernikov maximal subgroups, locally finite groups, 01 natural sciences

Hartley, B.

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Algebra and Logicarrow_drop_down

Algebra and Logic

Article . 1998 . Peer-reviewed

License: Springer TDM

Data sources: Crossref

zbMATH Open

Article . 1998

Data sources: zbMATH Open

https://dx.doi.org/10.1007/bf0...

Article

Data sources: Microsoft Academic Graph

On locally finite groups with a Chernikov maximal subgroup

On locally finite groups with Chernikov maximal subgroup

descriptionPublicationkeyboard_double_arrow_right Article 01 Jan 1998 English Publisher:Springer Science and Business Media LLCJournal:Algebra and Logic, volume 37, pages 56-58 (issn: 0002-5232, eissn: 1573-8302,

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Authors: Hartley, B.;

doi: 10.1007/bf02684085

On locally finite groups with a Chernikov maximal subgroup

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Abstract

The following theorem is proven: Let \(G\) be a locally finite group with Chernikov maximal subgroup \(H\) and let \(H\) contain no nontrivial normal subgroups of \(G\); then either \(G\) is finite or there exists an infinite normal elementary Abelian subgroup \(V\) of \(G\) such that \(G=VH\) and \(V\cap H=1\).

Keywords

Extensions, wreath products, and other compositions of groups, Maximal subgroups, Periodic groups; locally finite groups, Subgroup theorems; subgroup growth, Chernikov maximal subgroups, locally finite groups

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