| Title:
|
On the composition factors of a group with the same prime graph as $B_{n}(5)$ (English) |
| Author:
|
Babai, Azam |
| Author:
|
Khosravi, Behrooz |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
62 |
| Issue:
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2 |
| Year:
|
2012 |
| Pages:
|
469-486 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $G$ be a finite group. The prime graph of $G$ is a graph whose vertex set is the set of prime divisors of $|G|$ and two distinct primes $p$ and $q$ are joined by an edge, whenever $G$ contains an element of order $pq$. The prime graph of $G$ is denoted by $\Gamma (G)$. It is proved that some finite groups are uniquely determined by their prime graph. In this paper, we show that if $G$ is a finite group such that $\Gamma (G)=\Gamma (B_{n}(5))$, where $n\geq 6$, then $G$ has a unique nonabelian composition factor isomorphic to $B_{n}(5)$ or $C_{n}(5)$. (English) |
| Keyword:
|
prime graph |
| Keyword:
|
simple group |
| Keyword:
|
recognition |
| Keyword:
|
quasirecognition |
| MSC:
|
05C25 |
| MSC:
|
20D05 |
| MSC:
|
20D06 |
| MSC:
|
20D60 |
| idZBL:
|
Zbl 1249.20014 |
| idMR:
|
MR2990187 |
| DOI:
|
10.1007/s10587-012-0022-9 |
| . |
| Date available:
|
2012-06-08T09:46:43Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/142839 |
| . |
| Reference:
|
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