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 Algebra Discrete Math.: Year: Volume: Issue: Page: Find

 Algebra Discrete Math., 2015, Volume 19, Issue 1, Pages 1–7 (Mi adm501)

RESEARCH ARTICLE

On subgroups of finite exponent in groups

Orest D. Artemovych

Institute of Mathematics, Cracow University of Technology

Abstract: We investigate properties of groups with subgroups of finite exponent and prove that a non-perfect group $G$ of infinite exponent with all proper subgroups of finite exponent has the following properties:
$(1)$ $G$ is an indecomposable $p$-group,
$(2)$ if the derived subgroup $G'$ is non-perfect, then $G/G"$ is a group of Heineken-Mohamed type.
We also prove that a non-perfect indecomposable group $G$ with the non-perfect locally nilpotent derived subgroup $G'$ is a locally finite $p$-group.

Keywords: locally finite group, finitely generated group, exponent, group of Heineken-Mohamed type.

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Bibliographic databases:
MSC: 20F50, 20F26, 20E26
Revised: 23.02.2015
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Citation: Orest D. Artemovych, “On subgroups of finite exponent in groups”, Algebra Discrete Math., 19:1 (2015), 1–7

Citation in format AMSBIB
\Bibitem{Art15} \by Orest~D.~Artemovych \paper On subgroups of finite exponent in groups \jour Algebra Discrete Math. \yr 2015 \vol 19 \issue 1 \pages 1--7 \mathnet{http://mi.mathnet.ru/adm501} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=3376334} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000209846200001}