| Title:
|
A characterization of $C_2(q)$ where $q>5$ (English) |
| Author:
|
Iranmanesh, A. |
| Author:
|
Khosravi, B. |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
43 |
| Issue:
|
1 |
| Year:
|
2002 |
| Pages:
|
9-21 |
| . |
| Category:
|
math |
| . |
| Summary:
|
The order of every finite group $G$ can be expressed as a product of coprime positive integers $m_1,\dots, m_t$ such that $\pi (m_i)$ is a connected component of the prime graph of $G$. The integers $m_1,\dots, m_t$ are called the order components of $G$. Some non-abelian simple groups are known to be uniquely determined by their order components. As the main result of this paper, we show that the projective symplectic groups $C_2(q)$ where $q>5$ are also uniquely determined by their order components. As corollaries of this result, the validities of a conjecture by J.G. Thompson and a conjecture by W. Shi and J. Be for $C_2(q)$ with $q>5$ are obtained. (English) |
| Keyword:
|
prime graph |
| Keyword:
|
order component |
| Keyword:
|
finite group |
| Keyword:
|
simple group |
| MSC:
|
05C25 |
| MSC:
|
20D05 |
| MSC:
|
20D60 |
| MSC:
|
20G40 |
| idZBL:
|
Zbl 1068.20020 |
| idMR:
|
MR1903303 |
| . |
| Date available:
|
2009-01-08T19:19:01Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119296 |
| . |
| Reference:
|
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| . |
