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Paper   IPM / M / 748
School of Mathematics
Title:   A characterization of C2(q) where q > 5
Author(s):
 1 A. Iranmanesh 2 B. Khosravi
Status:   Published
Journal: Comment. Math. Univ. Carolin.
No.:  1
Vol.:  43
Year:  2002
Pages:   9-21
Supported by:  IPM
Abstract:
The order of every finite group G can be expressed as a product of coprime positive integers m1,…, mt such that π(mi) is a connected component of the prime graph of G. The integers m1,…, mt 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 C2(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 C2(q) with q > 5 are obtained.