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Sibirskii Matematicheskii Zhurnal, 2007, Volume 48, Number 4, Pages 742–759 (Mi smj1741)  
This article is cited in 43 scientific papers (total in 43 papers)

$X$-quasinormal subgroups

W. Guoa, A. N. Skibab, K. P. Shamc

a Department of Mathematics, Xuzhou Normal University, Xuzhou, P. R. China
b Francisk Skaryna Gomel State University, Faculty of Mathematics, Gomel, Belarus
c Depatrment of Mathematics, The Chinese University of Hong Kong, Hong Kong, P. R. China (SAR)
Full-text PDF (452 kB) Citations (43)
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Abstract: Considering two subgroups $A$ and $B$ of a group $G$ and $\varnothing\ne X\subseteq G$, we say that $A$ is $X$-permutable with $B$ if $AB^x=B^xA$ for some element $x\in X$. We use this concept to give new characterizations of the classes of solvable, supersolvable, and nilpotent finite groups.
Keywords: Sylow subgroup, supplement to a subgroup, maximal subgroup, nilpotent group, supersolvable group, solvable group, $X$-quasinormal subgroup.
Received: 26.01.2006
English version:
Siberian Mathematical Journal, 2007, Volume 48, Issue 4, Pages 593–605
DOI: https://doi.org/10.1007/s11202-007-0061-x
Bibliographic databases:
Language: Russian
Citation: W. Guo, A. N. Skiba, K. P. Sham, “$X$-quasinormal subgroups”, Sibirsk. Mat. Zh., 48:4 (2007), 742–759; Siberian Math. J., 48:4 (2007), 593–605
Citation in format AMSBIB
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    • This publication is cited in the following 43 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Сибирский математический журнал Siberian Mathematical Journal
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