The order of every finite group G can be expressed as a product
of coprime positive integers m_{1},…, m_{t} such that
π(m_{i}) is a connected component of the prime graph of G. The
integers m_{1},…, m_{t} are called the order components of G.
Some nonabelian 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.
Download TeX format
