Geodesic
On partially conjugate-permutable subgroups of finite groups
Problemy fiziki, matematiki i tehniki, no. 1 (2013), pp. 74-78

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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. 
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     author = {V. I. Murashko},
     title = {On partially conjugate-permutable subgroups of finite groups},
     journal = {Problemy fiziki, matematiki i tehniki},
     pages = {74--78},
     publisher = {mathdoc},
     number = {1},
     year = {2013},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/PFMT_2013_1_a12/}
}
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V. I. Murashko. On partially conjugate-permutable subgroups of finite groups. Problemy fiziki, matematiki i tehniki, no. 1 (2013), pp. 74-78. http://geodesic.mathdoc.fr/item/PFMT_2013_1_a12/