partially s-embedded minimal subgroups of finite groups
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abstract
suppose that $h$ is a subgroup of $g$, then $h$ is said to be $s$-permutable in $g$, if $h$ permutes with every sylow subgroup of $g$. if $hp=ph$ hold for every sylow subgroup $p$ of $g$ with $(|p|, |h|)=1$), then $h$ is called an $s$-semipermutable subgroup of $g$. in this paper, we say that $h$ is partially $s$-embedded in $g$ if $g$ has a normal subgroup $t$ such that $ht$ is $s$-permutable in $g$ and $hcap tleq h_{overline{s}g}$, where $h_{overline{s}g}$ is generated by all $s$-semipermutable subgroups of $g$ contained in $h$. we investigate the influence of some partially $s$-embedded minimal subgroups on the nilpotency and supersolubility of a finite group $g$. a series of known results in the literature are unified and generalized.
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Journal title:
international journal of group theoryPublisher: university of isfahan
ISSN 2251-7650
volume 2
issue 4 2013
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