| Title:
|
A solvability criterion for finite groups related to character degrees (English) |
| Author:
|
Miraali, Babak |
| Author:
|
Robati, Sajjad Mahmood |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
70 |
| Issue:
|
4 |
| Year:
|
2020 |
| Pages:
|
1205-1209 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $m>1$ be a fixed positive integer. In this paper, we consider finite groups each of whose nonlinear character degrees has exactly $m$ prime divisors. We show that such groups are solvable whenever $m>2$. Moreover, we prove that if $G$ is a non-solvable group with this property, then $m=2$ and $G$ is an extension of ${\rm A}_7$ or ${\rm S}_7$ by a solvable group. (English) |
| Keyword:
|
non-solvable group |
| Keyword:
|
solvable group |
| Keyword:
|
character degree |
| MSC:
|
20C15 |
| MSC:
|
20D10 |
| idZBL:
|
07285992 |
| idMR:
|
MR4181809 |
| DOI:
|
10.21136/CMJ.2020.0440-19 |
| . |
| Date available:
|
2020-11-18T09:52:18Z |
| Last updated:
|
2023-01-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/148424 |
| . |
| 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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| Reference:
|
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| Reference:
|
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| . |
