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\(M_p\)-groups not containing groups of quaternions. (English. Russian original) Zbl 1325.20032

Russ. Math. 58, No. 2, 13-23 (2014); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 2014, No. 2, 17-29 (2014).
From the text: In the main result of the paper, we establish a criterion of nonsimplicity of an infinite group under sufficiently weak restrictions imposed upon some series of subgroups. As consequences of the main result, we obtain a criterion for an infinite group to be an \(M_p\)-group and prove a theorem on the structure of a group without involutions with an element of prime order \(p\) which together with each conjugate element generates a finite subgroup, has finite primary centralizer, and normalizes some maximal complete abelian \(p\)-subgroup \(B\).

MSC:

20F50 Periodic groups; locally finite groups
20F22 Other classes of groups defined by subgroup chains
20F05 Generators, relations, and presentations of groups
20E07 Subgroup theorems; subgroup growth
20E25 Local properties of groups
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References:

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