Skip to content

Research at St Andrews

All simple groups with order from 1 million to 5 million are efficient

Research output: Contribution to journalArticle

Abstract

There is much interest in finding short presentations for the finite simple groups. Indeed it has been suggested that all these groups are efficient in a technical sense. In previous papers we produced nice efficient presentations for all except one of the simple groups with order less than one million. Here we show that all simple groups with order between 1 million and 5 million are efficient by giving efficient presentations for all of them. Apart from some linear groups these results are all new. We also show that some covering groups and some larger simple groups are efficient. We make substantial use of systems for computational group theory and, in particular, of computer implementations of coset enumeration to find and verify our presentations.
Close

Details

Original languageEnglish
Pages (from-to)17–30
Number of pages14
JournalInternational Journal of Group Theory
Volume3
Issue number1
StatePublished - Mar 2014

    Research areas

  • Efficient presentations, Simple groups, Coset enumeration

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

View graph of relations

Related by author

  1. 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

  2. Groups St Andrews 2009 in Bath, Volume 1

    Campbell, C. M., Quick, M., Robertson, E. F., Roney-Dougal, C. M., Smith, G. & Traustason, G. 2011 Cambridge University Press. 307 p. (London Mathematical Society Lecture Note Series 387)

    Research output: Book/ReportBook

  3. Groups St Andrews 2009 in Bath, Volume 2

    Campbell, C. M., Quick, M., Robertson, E. F., Roney-Dougal, C. M., Smith, G. C. & Traustason, G. 2011 Cambridge University Press. 304 p. (London Mathematical Society Lecture Note Series 388)

    Research output: Book/ReportBook

  4. Groups - St Andrews 1981 (new edition)

    Campbell, C. M. & Robertson, E. F. 2007 Cambridge University Press. 373 p. (London Mathematical Society Lecture Note Series 71)

    Research output: Book/ReportBook

  5. Groups St Andrews 2005, Volume 1

    Campbell, C. M., Quick, M., Robertson, E. F. & Smith, G. C. 2007 Cambridge University Press. 355 p. (London Mathematical Lecture Note Series 387)

    Research output: Book/ReportBook

ID: 107733283