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On locally finite groups with Chernikov maximal subgroup. (English. Russian original) Zbl 0941.20042
Algebra Logika 37, No. 1, 101-106 (1998); translation in Algebra Logic 37, No. 1, 56-58 (1998).
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 \(V\cap H=1\).
MSC:
20F50 Periodic groups; locally finite groups
20E28 Maximal subgroups
20E22 Extensions, wreath products, and other compositions of groups
20E07 Subgroup theorems; subgroup growth
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