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arXiv · 1507.00854

A note on the probability of generating alternating or symmetric groups

Luke Morgan·Colva M. Roney-Dougal
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Abstract

We improve on recent estimates for the probability of generating the alternating and symmetric groups $\mathrm{Alt}(n)$ and $\mathrm{Sym}(n)$. 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 $h(\mathrm{Alt}(n))$ such that a direct product of $h(\mathrm{Alt}(n))$ copies of $\mathrm{Alt}(n)$ can be generated by two elements.

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Luke Morgan, Colva M. Roney-Dougal. 2015-07-03. A note on the probability of generating alternating or symmetric groups. https://doi.org/10.1007/s00013-015-0796-8

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