A note on the probability of generating alternating or symmetric groups
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We improve on recent estimates for the probability of generating the alternating and symmetric groups A n and S n . In particular, we find the sharp lower bound if the probability is given by a quadratic in n −1. This leads to improved bounds on the largest number h(A n ) such that a direct product of h(A n ) copies of A n can be generated by two elements.
KeywordsSymmetric group Alternating group Generation Probability
Mathematics Subject Classification20B30 20P05
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