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We proved that the symplectic groups , where is a Fermat prime number is uniquely determined by its order, the first largest element orders and the second largest element orders.
Let be a finite group. The main supergraph is a graph with vertex set in which two vertices and are adjacent if and only if or . In this paper, we will show that if and only if . As a main consequence of our result we conclude that Thompson’s problem is true for the small Ree group .
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