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Paper IPM / M / 2333  


Abstract:  
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. It is
known that some nonabelian 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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