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.
@article{119296,
author = {Ali Iranmanesh and Behrooz Khosravi},
title = {A characterization of $C\_2(q)$ where $q>5$},
journal = {Commentationes Mathematicae Universitatis Carolinae},
volume = {43},
year = {2002},
pages = {9-21},
zbl = {1068.20020},
mrnumber = {1903303},
language = {en},
url = {http://dml.mathdoc.fr/item/119296}
}
Iranmanesh, Ali; Khosravi, Behrooz. A characterization of $C_2(q)$ where $q>5$. Commentationes Mathematicae Universitatis Carolinae, Tome 43 (2002) pp. 9-21. http://gdmltest.u-ga.fr/item/119296/
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