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Title

All simple groups with order from ۱ million to ۵ million are efficient

Year: 1393
COI: JR_THEGR-3-1_003
Language: EnglishView: 84
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Authors

Colin Campbell - School of Mathematics and Statistics, University of St Andrews
George Havas - Centre for Discrete Mathematics and Computing, School of Information Technology and Electrical Engineering, The University of Queensland
Colin Ramsay - Centre for Discrete Mathematics and Computing, School of Information Technology and Electrical Engineering, The University of Queensland
Edmund Robertson - School of Mathematics and Statistics, University of St Andrews

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 ۱ million and ۵ 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.

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Paper COI Code

This Paper COI Code is JR_THEGR-3-1_003. Also You can use the following address to link to this article. This link is permanent and is used as an article registration confirmation in the Civilica reference:

https://civilica.com/doc/1199601/

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Campbell, Colin and Havas, George and Ramsay, Colin and Robertson, Edmund,1393,All simple groups with order from ۱ million to ۵ million are efficient,https://civilica.com/doc/1199601

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  • W. Bosma, J. Cannon and C. Playoust (1997). The Magma ...
  • J. N. Bray, M. D. E. Conder, C. R. Leedham-Green ...
  • C. M. Campbell, G. Havas, C. Ramsay and E. F. ...
  • C. M. Campbell, G. Havas, C. Ramsay and E. F. ...
  • C. M. Campbell and E. F. Robertson (1980). A deficiency ...
  • C. M. Campbell and E. F. Robertson (1988). Computing with ...
  • C. M. Campbell, E. F. Robertson and P. D. Williams ...
  • M. Conder, G. Havas and M. F. Newman (2011). On ...
  • J. H. Conway, R. T. Curtis, S. P. Norton, R. ...
  • D. B. A. Epstein (1961). Finite presentations of groups and ...
  • The GAP~Group (2012). GAP Groups, Algorithms, and Programming ...
  • R. M. Guralnick, W. M. Kantor, M. Kassabov and A. ...
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  • G. Havas and D. F. Holt (2010). On Coxeter's families ...
  • G. Havas and C. Ramsay (2001). Coset enumeration: ACE version ...
  • G. Havas and C. Ramsay (2003). Short balanced presentations of ...
  • G. Havas and C. Ramsay (2003). Breadth-first search and the ...
  • I. Korchagina and A. Lubotzky (2006). On presentations and second ...
  • J. G.~Sunday (1972). Presentations of the groups SL(2,m) and PSL(2,m). ...
  • J. S. Wilson (2006). Finite axiomatization of finite soluble groups. ...
  • R. Wilson, P. Walsh, J. Tripp, Ibrahim Suleiman, Richard Parker, ...

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