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A note on the probability of generating alternating or symmetric groups

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Date
09/2015
Author
Morgan, Luke
Roney-Dougal, Colva Mary
Keywords
Symmetric group
Alternating group
Generation
Probability
QA Mathematics
T-NDAS
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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
DOI
https://doi.org/10.1007/s00013-015-0796-8
ISSN
0003-889X
Type
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.
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  • University of St Andrews Research
URI
http://hdl.handle.net/10023/9348

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