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PFMT, 2010, Issue 2(3), Pages 54–61 (Mi pfmt157)  

MATHEMATICS

The influence of $s$-$c$-permutably embedded subgroups on the structure of finite groups

Fan Chenga, Jianhong Huangba, Wenjuan Niua, Lifang Maa

a Xuzhou Normal University, Xuzhou, China
b University of Science and Technology of China, Hefei, China

Abstract: A subgroup $H$ of a group $G$ is said to be $s$-$c$-permutably embedded in $G$ if every Sylow subgroup of $H$ is a Sylow subgroup of some $s$-conditionally permutable subgroup of $G$. In this paper, some new characterizations for a finite group to be $p$-supersoluble or $p$-nilpotent are obtained under the assumption that some of its maximal subgroups or 2-maximal subgroups of Sylow subgroups are $s$-$c$-permutably embedded. A series of known results are generalized.

Keywords: finite group, $s$-$c$-permutably embedded subgroups, 2-maximal subgroups, Sylow subgroup, $p$-supersoluble group, $p$-nilpotent group

Full text: PDF file (475 kB)
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UDC: 512.542
Received: 12.05.2010
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Citation: Fan Cheng, Jianhong Huang, Wenjuan Niu, Lifang Ma, “The influence of $s$-$c$-permutably embedded subgroups on the structure of finite groups”, PFMT, 2010, no. 2(3), 54–61

Citation in format AMSBIB
\Bibitem{FanHuaWen10}
\by Fan Cheng, Jianhong Huang, Wenjuan Niu, Lifang Ma
\paper The influence of $s$-$c$-permutably embedded subgroups on the structure of finite groups
\jour PFMT
\yr 2010
\issue 2(3)
\pages 54--61
\mathnet{http://mi.mathnet.ru/pfmt157}


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