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A note on the probability of generating alternating or symmetric groups

Research output: Contribution to journalArticlepeer-review

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.

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Original languageEnglish
Pages (from-to)201-204
Number of pages4
JournalArchiv der Mathematik
Volume105
Issue number3
Early online date21 Aug 2015
DOIs
Publication statusPublished - Sep 2015

    Research areas

  • Symmetric group, Alternating group, Generation, Probability

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