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Paper IPM / M / 11467  


Abstract:  
Let G be a finite group. The prime graph Γ(G) of G is defined as follows. The vertices of Γ(G) are the primes dividing the order of G and two distinct vertices p,p′ are joined by an edge if there is an element in G of order pp′. In this paper we give a survey about this question that which groups have the same prime graph. It is proved that some finite groups are uniquely determined by their prime graph. Applications of this result to the problem of recognition of finite groups by the set of element orders are also considered.
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