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Paper IPM / M / 8002  


Abstract:  
The noncommuting graph ∇(G) of a nonabelian finite group
G is defined as follows: The vertices of ∇(G) are
represented by the noncentral elements of G, and two distinct
vertices x and y are joined by an edge if xy ≠ yx. In [2],
it was conjectured that: Let G and H be two nonabelian finite
groups such that ∇(G) ≅ ∇(H), then G=H. In
this article we give, some counterexamples to this conjecture.
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