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Let $G$ be a finite group. The order of $G$ is the product of
coprime positive integers which is called the order components of
$G$. It was proved that some non-abelian simple groups are
uniquely determined by their order components. As the main result
of this paper, we show that the simple groups $PSU(17,q)$ are also
uniquely determined by their order components. As corollaries of
this result, the validity of a conjecture of J. G. Thompson and a
conjecture of W. Shi. and J. Bi both on $PSU(17,q)$ is obtained.
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