Geodesic
On decomposability of finite groups
Czechoslovak Mathematical Journal, Tome 67 (2017) no. 3, pp. 827-837.

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Let $G$ be a finite group. A normal subgroup $N$ of $G$ is a union of several $G$-conjugacy classes, and it is called $n$-decomposable in $G$ if it is a union of $n$ distinct $G$-conjugacy classes. In this paper, we first classify finite non-perfect groups satisfying the condition that the numbers of conjugacy classes contained in its non-trivial normal subgroups are two consecutive positive integers, and we later prove that there is no non-perfect group such that the numbers of conjugacy classes contained in its non-trivial normal subgroups are 2, 3, 4 and 5.
DOI : 10.21136/CMJ.2017.0197-16
Classification : 20D10, 20E45
Keywords: non-perfect group; $G$-conjugacy class; $n$-decomposable group 
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Chen, Ruifang; Zhao, Xianhe. On decomposability of finite groups. Czechoslovak Mathematical Journal, Tome 67 (2017) no. 3, pp. 827-837. doi : 10.21136/CMJ.2017.0197-16. http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2017.0197-16/

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