RESEARCH ARTICLE

Minimal non-$PC$-groups

Orest D. Artemovych

Institute of Mathematics, Cracow University of Technology, ul. Warszawska 24, Cracow 31-155 POLAND

Abstract: The purpose of this paper is to prove that a non-perfect group $G$ is a minimal non-$PC$-group if and only if it is a minimal non-$FC$-group. It is shown that a perfect locally graded minimal non-$PC$-group is an indecomposable countable locally finite $p$-group.

Keywords: $PC$-group, $FC$-group.

MSC: 20F24, 20E45

Received: 01.02.2014
Revised: 07.02.2014

Language: English

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