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The order of every finite group $G$ can be expressed as a product
of coprime positive integers $m_1, ..., m_t$ such that $\pi (m_i)$
is a connected component of the prime graph of $G.$ The integers
$m_1, ... , m_t$ are called the order components of $G$. It is
known that some non-abelian simple groups are uniquely determined
by their order components. As the main result of this paper, we
show that groups $PSU_5(q)$ 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. Be
both on $PSU_5 (q)$ is obtained.
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