Geodesic
On decomposability of finite groups
Czechoslovak Mathematical Journal, Tome 67 (2017) no. 3, pp. 827-837 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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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     author = {Chen, Ruifang and Zhao, Xianhe},
     title = {On decomposability of finite groups},
     journal = {Czechoslovak Mathematical Journal},
     pages = {827--837},
     year = {2017},
     volume = {67},
     number = {3},
     doi = {10.21136/CMJ.2017.0197-16},
     mrnumber = {3697920},
     zbl = {06770134},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2017.0197-16/}
}
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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

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