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- W2526555199 abstract "Let $sigma ={sigma_{i} | iin I}$ be some partition of the set of all primes $Bbb{P}$, $G$ a finite group and $sigma (G) ={sigma_{i} |sigma_{i}cap pi (G)ne emptyset }$. A set ${cal H}$ of subgroups of $G$ is said to be a emph{complete Hall $sigma $-set} of $G$ if every member $ne 1$ of ${cal H}$ is a Hall $sigma_{i}$-subgroup of $G$ for some $sigma_{i}in sigma $ and ${cal H}$ contains exact one Hall $sigma_{i}$-subgroup of $G$ for every $sigma_{i}in sigma (G)$. A subgroup $H$ of $G$ is said to be: emph{${sigma}$-semipermutable in $G$ with respect to ${cal H}$} if $HH_{i}^{x}=H_{i}^{x}H$ for all $xin G$ and all $H_iin {cal H}$ such that $(|H|, |H_{i}|)=1$; emph{${sigma}$-semipermutable in $G$} if $H$ is ${sigma}$-semipermutable in $G$ with respect to some complete Hall $sigma $-set of $G$. We study the structure of $G$ being based on the assumption that some subgroups of $G$ are ${sigma}$-semipermutable in $G$." @default.
- W2526555199 created "2016-10-07" @default.
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- W2526555199 date "2016-09-28" @default.
- W2526555199 modified "2023-09-27" @default.
- W2526555199 title "On $sigma$-semipermutable subgroups of finite groups" @default.
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- W2526555199 doi "https://doi.org/10.48550/arxiv.1609.08815" @default.
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