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On s-semipermutable or s-quasinormally Embedded Subgroups of Finite Groups
Published online by Cambridge University Press: 20 November 2018
Abstract
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Suppose that 
$G$ is a finite group and 
$H$ is a subgroup of $G$. $H$ is said to be 
$s$-semipermutable in $G$ if 
$H{{G}_{p}}\,=\,{{G}_{p}}H$ for any Sylow 
$p$-subgroup 
${{G}_{p}}$ of $G$ with 
$\left( p,\,\left| H \right| \right)\,=\,1$; $H$ is said to be $s$-quasinormally embedded in $G$ if for each prime $p$ dividing the order of $H$, a Sylow $p$-subgroup of $H$ is also a Sylow $p$-subgroup of some $s$-quasinormal subgroup of $G$. In every non-cyclic Sylow subgroup 
$P$ of $G$ we fix some subgroup 
$D$ satisfying 
$1\,<\,\left| D \right|\,<\,\left| P \right|$ and study the structure of $G$ under the assumption that every subgroup $H$ of $P$ with 
$\left| H \right|\,=\,\left| D \right|$ is either $s$-semipermutable or $s$-quasinormally embedded in $G$. Some recent results are generalized and unified.
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- Copyright © Canadian Mathematical Society 2015
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