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Sibirsk. Mat. Zh., 2007, Volume 48, Number 3, Pages 674–688 (Mi smj56)  

This article is cited in 5 scientific papers (total in 5 papers)

Finite groups with $C$-quasinormal subgroups

A. N. Skibaa, O. V. Titovb

a Francisk Skorina Gomel State University
b Belarusian State University of Transport

Abstract: Consider some finite group $G$ and a finite subgroup $H$ of $G$. Say that $H$ is $c$-quasinormal in $G$ if $G$ has a quasinormal subgroup $T$ such that $HT=G$ and $T\cap H$ is quasinormal in $G$. Given a noncyclic Sylow subgroup $P$ of $G$, we fix some subgroup $D$ such that $1<|D|<|P|$ and study the structure of $G$ under the assumption that all subgroups $H$ of $P$ of the same order as $D$, having no supersolvable supplement in $G$, are $c$-quasinormal in $G$.

Keywords: Sylow subgroup, supplement to a subgroup, supersolvable group, quasinormal subgroup, saturated formation.

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English version:
Siberian Mathematical Journal, 2007, 48:3, 544–554

Bibliographic databases:

UDC: 512.54
Received: 22.06.2006
Revised: 04.02.2007

Citation: A. N. Skiba, O. V. Titov, “Finite groups with $C$-quasinormal subgroups”, Sibirsk. Mat. Zh., 48:3 (2007), 674–688; Siberian Math. J., 48:3 (2007), 544–554

Citation in format AMSBIB
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\paper Finite groups with $C$-quasinormal subgroups
\jour Sibirsk. Mat. Zh.
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\pages 674--688
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\transl
\jour Siberian Math. J.
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\pages 544--554
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    This publication is cited in the following articles:
    1. Miao L., Lempken W., “On $\mathscr M$-supplemented subgroups of finite groups”, J. Group Theory, 12:2 (2009), 271–287  crossref  mathscinet  zmath  isi  elib  scopus
    2. Miao L., “On weakly $\mathscr M$-supplemented subgroups of Sylow $p$-subgroups of finite groups”, Glasg. Math. J., 53:2 (2011), 401–410  crossref  mathscinet  zmath  isi  elib  scopus
    3. Shen Zh., Shi W., “The influence of SNS-permutability of some subgroups on the structure of finite groups”, Publ. Math. Debrecen, 78:1 (2011), 159–168  crossref  mathscinet  zmath  adsnasa  isi  scopus
    4. Miao L., Li B., “On $\mathscr F$-quasinormal primary subgroups of finite groups”, Comm. Algebra, 39:10 (2011), 3515–3525  crossref  mathscinet  zmath  isi  elib  scopus
    5. Zhencai Shen, Shirong Li, Jinshan Zhang, “On SS-Quasinormal and S-Quasinormally Embedded Subgroups of Finite Groups”, Math. Notes, 95:2 (2014), 270–279  mathnet  crossref  crossref  mathscinet  isi  elib
  • Сибирский математический журнал Siberian Mathematical Journal
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