A note on the probability of generating alternating or symmetric groups
Abstract
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.
Citation
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 . https://doi.org/10.1007/s00013-015-0796-8
Publication
Archiv der Mathematik
Status
Peer reviewed
ISSN
0003-889XType
Journal article
Rights
© 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
Description
The research of the first author is supported by the Australian Research Council grant DP120100446.Collections
Items in the St Andrews Research Repository are protected by copyright, with all rights reserved, unless otherwise indicated.