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 An and Sn. 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(An) such that a direct product of h(An) copies of An can be generated by two elements.
Morgan , L & Roney-Dougal , C M 2015 , ' A note on the probability of generating alternating or symmetric groups ' Archiv der Mathematik , vol 105 , no. 3 , pp. 201-204 . DOI: 10.1007/s00013-015-0796-8
Archiv der Mathematik
© 2015, Publisher / the Author(s). This work is made available online in accordance with the publisher’s policies. This is the author created, accepted version manuscript following peer review and may differ slightly from the final published version. The final published version of this work is available at http://link.springer.com/article/10.1007/s00013-015-0796-8
The research of the first author is supported by the Australian Research Council grant DP120100446.