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Sibirsk. Mat. Zh., 2012, Volume 53, Number 3, Pages 558–565 (Mi smj2345)  

This article is cited in 4 scientific papers (total in 4 papers)

On finite $X$-decomposable groups for $X=\{1,2,4\}$

X. Guoa, J. Lia, K. P. Shumb

a Department of Mathematics, Shanghai University, Shanghai, P. R. China
b Institute of Mathematics, Yunnan University, Kunming, P. R. China

Abstract: A normal subgroup $N$ of a finite group $G$ is called an $n$-decomposable subgroup if $N$ is a union of $n$ distinct conjugacy classes of $G$. Each finite nonabelian nonperfect group is proved to be isomorphic to $Q_{12}$, or $Z_2\times A_4$, or $G=\langle a,b,c\mid a^{11}=b^5=c^2=1, b^{-1}ab=a^4, c^{-1}ac=a^{-1}, c^{-1}bc=b^{-1}\rangle$ if every nontrivial normal subgroup is $2$- or $4$-decomposable.

Keywords: $n$-decomposable, $X$-decomposable, $G$-conjugacy class.

Full text: PDF file (308 kB)
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English version:
Siberian Mathematical Journal, 2012, 53:3, 444–449

Bibliographic databases:

UDC: 512.54
Received: 22.02.2011

Citation: X. Guo, J. Li, K. P. Shum, “On finite $X$-decomposable groups for $X=\{1,2,4\}$”, Sibirsk. Mat. Zh., 53:3 (2012), 558–565; Siberian Math. J., 53:3 (2012), 444–449

Citation in format AMSBIB
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\by X.~Guo, J.~Li, K.~P.~Shum
\paper On finite $X$-decomposable groups for $X=\{1,2,4\}$
\jour Sibirsk. Mat. Zh.
\yr 2012
\vol 53
\issue 3
\pages 558--565
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\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2978574}
\transl
\jour Siberian Math. J.
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\vol 53
\issue 3
\pages 444--449
\crossref{https://doi.org/10.1134/S0037446612020255}
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Guo X., Chen R., “on Finite X-Decomposable Groups For X = (1,2,3,4)”, Bull. Iran Math. Soc., 40:5 (2014), 1243–1262  mathscinet  zmath  isi
    2. R. Chen, X. Zhao, “On decomposability of finite groups”, Czech. Math. J., 67:3 (2017), 827–837  crossref  mathscinet  zmath  isi  scopus
    3. R. Chen, X. Guo, K. P. Shum, “$X$-decomposable finite groups for $X=\{1,m,m+1,m+2\}$”, Siberian Math. J., 58:5 (2017), 899–906  mathnet  crossref  crossref  isi  elib
    4. Ashrafi A.R., Koorepazan-Moftakhar F., “On Normal Graph of a Finite Group”, Filomat, 32:11 (2018), 4047–4059  crossref  mathscinet  isi  scopus
  • Сибирский математический журнал Siberian Mathematical Journal
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