| Title:
|
On the number of isomorphism classes of derived subgroups (English) |
| Author:
|
Taghvasani, Leyli Jafari |
| Author:
|
Marzang, Soran |
| Author:
|
Zarrin, Mohammad |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
69 |
| Issue:
|
3 |
| Year:
|
2019 |
| Pages:
|
665-670 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We show that a finite nonabelian characteristically simple group $G$ satisfies $n=|\pi (G)|+2$ if and only if $G\cong A_5$, where $n$ is the number of isomorphism classes of derived subgroups of $G$ and $\pi (G)$ is the set of prime divisors of the group $G$. Also, we give a negative answer to a question raised in M. Zarrin (2014). (English) |
| Keyword:
|
derived subgroup |
| Keyword:
|
simple group |
| MSC:
|
20F24 |
| idZBL:
|
Zbl 07088811 |
| idMR:
|
MR3989273 |
| DOI:
|
10.21136/CMJ.2018.0464-17 |
| . |
| Date available:
|
2019-07-24T11:16:30Z |
| Last updated:
|
2021-10-04 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/147784 |
| . |
| 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:
|
[9] Longobardi, P., Maj, M., Robinson, D. J. S., Smith, H.: On groups with two isomorphism classes of derived subgroups.Glasg. Math. J. 55 (2013), 655-668. Zbl 1287.20046, MR 3084668, 10.1017/S0017089512000821 |
| Reference:
|
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| Reference:
|
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| . |
