Skip to content

Research at St Andrews

A note on the probability of generating alternating or symmetric groups

Research output: Contribution to journalArticle

DOI

Open Access permissions

Open

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.

Close

Details

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

    Research areas

  • Symmetric group, Alternating group, Generation, Probability

Discover related content
Find related publications, people, projects and more using interactive charts.

View graph of relations

Related by author

  1. Generating sets of finite groups

    Cameron, P. J., Lucchini, A. & Roney-Dougal, C. M. 2 Apr 2017 In : Transactions of the American Mathematical Society.

    Research output: Contribution to journalArticle

  2. On the generating graph of a simple group

    Lucchini, A., Maroti, A. & Roney-Dougal, C. M. 26 Sep 2016 In : Journal of the Australian Mathematical Society. First View

    Research output: Contribution to journalArticle

  3. Coprime invariable generation and minimal-exponent groups

    Detomi, E., Lucchini, A. & Roney-Dougal, C. M. Aug 2015 In : Journal of Pure and Applied Algebra. 219, 8, p. 3453-3465 13 p.

    Research output: Contribution to journalArticle

  4. An explicit upper bound for the Helfgott delta in SL(2,p)

    Button, J. & Roney-Dougal, C. 1 Jan 2015 In : Journal of Algebra. 421, p. 493-511 19 p.

    Research output: Contribution to journalArticle

  5. Groups St Andrews 2013

    Campbell, C. M., Robertson, E. F., Quick, M. & Roney-Dougal, C. M. 2015 Cambridge: Cambridge University Press. 492 p. (London Mathematical Society Lecture Note Series 422)

    Research output: Book/ReportBook

Related by journal

  1. Orbital Graphs

    Jefferson, C., Pfeiffer, M. & Waldecker, R. 13 Mar 2017 In : Archiv der Mathematik.

    Research output: Contribution to journalArticle

  2. Finite groups are big as semigroups

    Dolinka, I. & Ruskuc, N. Sep 2011 In : Archiv der Mathematik. 97, 3, p. 209-217 9 p.

    Research output: Contribution to journalArticle

  3. Finite 3-groups of class 3 whose elements commute with their automorphic images

    Abdollahi, A., Faghihi, A., Linton, S. A. & O'Brien, E. A. 2010 In : Archiv der Mathematik. 95, 1, p. 1-7 7 p.

    Research output: Contribution to journalArticle

  4. A finitely presented monoid with a non-finitely generated group of units

    Carvalho, C. A. & Ruskuc, N. Aug 2007 In : Archiv der Mathematik. 89, 2, p. 109-113 5 p.

    Research output: Contribution to journalArticle

ID: 223509214