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|Paper IPM / M / 748||
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.
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