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This article is cited in 7 scientific papers (total in 7 papers)
On a periodic part of a Shunkov group saturated with wreathed groups
A. A. Shlepkin Institute of Space and Information Technologies, Siberian Federal University
Abstract:
A group G is saturated with groups from a set of groups X if any finite subgroup K of G is contained in a subgroup of G isomorphic to some group from X. A group G is called a Shunkov group (a conjugately biprimitively finite group) if, for any finite subgroup H of G, any two conjugate elements of prime order in the quotient group NG(H)/h generate a finite group. Let G be a group. If all elements of finite orders from G are contained in a periodic subgroup of G, then it is called a periodic part of G and is denoted by t(G). It is known that a Shunkov group may have no periodic part. The existence of a periodic part of a Shunkov group saturated with finite wreathed groups is proved and the structure of the periodic part is established.
Keywords:
group saturated with a set of groups, Shunkov group.
Received: 05.06.2018
Citation:
A. A. Shlepkin, “On a periodic part of a Shunkov group saturated with wreathed groups”, Trudy Inst. Mat. i Mekh. UrO RAN, 24, no. 3, 2018, 281–285
Linking options:
https://www.mathnet.ru/eng/timm1569 https://www.mathnet.ru/eng/timm/v24/i3/p281
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