Numerical bounds for the exterior degree of finite simple groups

Abstract The exterior degree of a finite group G is the probability that a pair (x, y) of elements x, y chosen uniformly at random in G satisfies where is the operator of nonabelian exterior square and neutral element in The probability d(G) that two elements of G commute is related to Of course, d(G) = 1 iff G is abelian, but iff G is cyclic, so we detect cyclic groups when is close to 1. We present new numerical results for the exterior degree of finite simple groups.

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