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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.

MSC: 20F50, 20F26, 20E26

Received: 03.12.2014
Revised: 23.02.2015

Language: English

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