On weakly s -permutably embedded subgroups

Changwen Li

Commentationes Mathematicae Universitatis Carolinae (2011)

  • Volume: 52, Issue: 1, page 21-29
  • ISSN: 0010-2628

Abstract

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Suppose G is a finite group and H is a subgroup of G . H is said to be s -permutably embedded in G if for each prime p dividing | H | , a Sylow p -subgroup of H is also a Sylow p -subgroup of some s -permutable subgroup of G ; H is called weakly s -permutably embedded in G if there are a subnormal subgroup T of G and an s -permutably embedded subgroup H s e of G contained in H such that G = H T and H ∩ T ≤ H s e . We investigate the influence of weakly s -permutably embedded subgroups on the p -nilpotency and p -supersolvability of finite groups.

How to cite

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Li, Changwen. "On weakly $s$-permutably embedded subgroups." Commentationes Mathematicae Universitatis Carolinae 52.1 (2011): 21-29. <http://eudml.org/doc/246816>.

@article{Li2011,
abstract = {Suppose $G$ is a finite group and $H$ is a subgroup of $G$. $H$ is said to be $s$-permutably embedded in $G$ if for each prime $p$ dividing $|H|$, a Sylow $p$-subgroup of $H$ is also a Sylow $p$-subgroup of some $s$-permutable subgroup of $G$; $H$ is called weakly $s$-permutably embedded in $G$ if there are a subnormal subgroup $T$ of $G$ and an $s$-permutably embedded subgroup $H_\{se\}$ of $G$ contained in $H$ such that $G=HT$ and $H\cap T\le H_\{se\}$. We investigate the influence of weakly $s$-permutably embedded subgroups on the $p$-nilpotency and $p$-supersolvability of finite groups.},
author = {Li, Changwen},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {weakly $s$-permutably embedded subgroups; $p$-nilpotent; $n$-maximal subgroup; finite groups; weakly -permutably embedded subgroups; -nilpotent groups; maximal subgroups; subnormal subgroups; nilpotency; supersolvability},
language = {eng},
number = {1},
pages = {21-29},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {On weakly $s$-permutably embedded subgroups},
url = {http://eudml.org/doc/246816},
volume = {52},
year = {2011},
}

TY - JOUR
AU - Li, Changwen
TI - On weakly $s$-permutably embedded subgroups
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2011
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 52
IS - 1
SP - 21
EP - 29
AB - Suppose $G$ is a finite group and $H$ is a subgroup of $G$. $H$ is said to be $s$-permutably embedded in $G$ if for each prime $p$ dividing $|H|$, a Sylow $p$-subgroup of $H$ is also a Sylow $p$-subgroup of some $s$-permutable subgroup of $G$; $H$ is called weakly $s$-permutably embedded in $G$ if there are a subnormal subgroup $T$ of $G$ and an $s$-permutably embedded subgroup $H_{se}$ of $G$ contained in $H$ such that $G=HT$ and $H\cap T\le H_{se}$. We investigate the influence of weakly $s$-permutably embedded subgroups on the $p$-nilpotency and $p$-supersolvability of finite groups.
LA - eng
KW - weakly $s$-permutably embedded subgroups; $p$-nilpotent; $n$-maximal subgroup; finite groups; weakly -permutably embedded subgroups; -nilpotent groups; maximal subgroups; subnormal subgroups; nilpotency; supersolvability
UR - http://eudml.org/doc/246816
ER -

References

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