| Title:
|
On decomposability of finite groups (English) |
| Author:
|
Chen, Ruifang |
| Author:
|
Zhao, Xianhe |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
67 |
| Issue:
|
3 |
| Year:
|
2017 |
| Pages:
|
827-837 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
non-perfect group |
| Keyword:
|
$G$-conjugacy class |
| Keyword:
|
$n$-decomposable group |
| MSC:
|
20D10 |
| MSC:
|
20E45 |
| idZBL:
|
Zbl 06770134 |
| idMR:
|
MR3697920 |
| DOI:
|
10.21136/CMJ.2017.0197-16 |
| . |
| Date available:
|
2017-09-01T12:27:17Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/146863 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
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| Reference:
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| Reference:
|
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| Reference:
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| Reference:
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| . |
