A note on the probability of generating alternating or symmetric groups

Morgan, Luke; Roney-Dougal, Colva Mary

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Date

09/2015

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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.

Collections

University of St Andrews Research

URI

http://hdl.handle.net/10023/9348