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JOURNALS // Problemy Fiziki, Matematiki i Tekhniki (Problems of Physics, Mathematics and Technics) // Archive

PFMT, 2013 Issue 1(14), Pages 74–78 (Mi pfmt225)

MATHEMATICS

On partially conjugate-permutable subgroups of finite groups

V. I. Murashko

F. Scorina Gomel State University, Gomel

Abstract: Let $R$ be a subgroup of a group $G$. We shall call a subgroup $H$ of $G$ the $R$-conjugate-permutable subgroup if $HH^r=H^rH$ for all $r\in R$. In this work the properties and the influence of $R$-conjugate-permutable subgroups (maximal, Sylow, cyclic primary) on the structure of finite groups are studied. As $R$ we consider the Fitting subgroup $F(G)$, quasinilpotent radical $F^*(G)$ and the generalized Fitting subgroup $\tilde{F}(G)$ that was introduced by P. Shmid. In particular, it was shown that group $G$ is nilpotent iff all its maximal subgroups are $\tilde{F}(G)$-conjugate-permutable.

Keywords: finite group, nilpotent group, $R$-conjugate-permutable subgroup, conjugate-permutable subgroup, the Fitting subgroup.

UDC: 512.542

Received: 28.12.2012

Language: English



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