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

This article is cited in 1 scientific paper (total in 1 paper)

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
Received: 03.12.2014
Revised: 23.02.2015
Language:

Citation: Orest D. Artemovych, “On subgroups of finite exponent in groups”, Algebra Discrete Math., 19:1 (2015), 1–7

Citation in format AMSBIB
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\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}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. M. Bouchelaghem, N. Trabelsi, “Groups whose proper subgroups of infinite rank have polycyclic-by-finite conjugacy classes”, Int. J. Group Theory, 5:3 (2016), 61–67  mathscinet  isi
  • Algebra and Discrete Mathematics
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