| Title:
|
Groups satisfying the two-prime hypothesis with a composition factor isomorphic to PSL$_2(q)$ for $q\geq 7$ (English) |
| Author:
|
Lewis, Mark L. |
| Author:
|
Liu, Yanjun |
| Author:
|
Tong-Viet, Hung P. |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
68 |
| Issue:
|
4 |
| Year:
|
2018 |
| Pages:
|
921-941 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $G$ be a finite group and write ${\rm cd} (G)$ for the degree set of the complex irreducible characters of $G$. The group $G$ is said to satisfy the two-prime hypothesis if for any distinct degrees $a, b \in {\rm cd} (G)$, the total number of (not necessarily different) primes of the greatest common divisor $\gcd (a, b)$ is at most $2$. We prove an upper bound on the number of irreducible character degrees of a nonsolvable group that has a composition factor isomorphic to PSL$_2 (q)$ for $q \geq 7$. (English) |
| Keyword:
|
character degrees |
| Keyword:
|
prime divisors |
| MSC:
|
20C15 |
| MSC:
|
20D05 |
| idZBL:
|
Zbl 07031688 |
| idMR:
|
MR3881887 |
| DOI:
|
10.21136/CMJ.2018.0027-17 |
| . |
| Date available:
|
2018-12-07T06:17:23Z |
| Last updated:
|
2021-01-04 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/147512 |
| . |
| 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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| . |
