|
Problemy Fiziki, Matematiki i Tekhniki (Problems of Physics, Mathematics and Technics), 2013, Issue 2(15), Pages 35–38
(Mi pfmt236)
|
|
|
|
MATHEMATICS
Permuteral subgroups and their applications in finite groups
A. F. Vasil'eva, V. A. Vasil'eva, T. I. Vasil'evab a F. Scorina Gomel State University, Gomel
b Belarusian State University of Transport, Gomel
Abstract:
Let $H$ be a subgroup of a group $G$. The permutizer of $H$ in $G$ is the subgroup $P_G(H)=\langle x\in G | \langle x\rangle H=H\langle x\rangle\rangle$. The subgroup $H$ of a group $G$ is called permuteral in $G$, if $P_G(H)=G$; strongly permuteral in $G$, if $P_U(H)=U$ whenever $H\leqslant U\leqslant G$. The properties of finite groups with given systems of permuteral and strongly permuteral subgroups are obtained. New criteria of
w-supersolubility and supersolubility of groups are received.
Keywords:
finite group, permutizer of a subgroup, permuteral subgroup, supersoluble group, w-supersoluble group, $\mathbf{P}$-subnormal subgroup.
Received: 25.04.2013
Citation:
A. F. Vasil'ev, V. A. Vasil'ev, T. I. Vasil'eva, “Permuteral subgroups and their applications in finite groups”, PFMT, 2013, no. 2(15), 35–38
Linking options:
https://www.mathnet.ru/eng/pfmt236 https://www.mathnet.ru/eng/pfmt/y2013/i2/p35
|
|