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Original Article

On the Efficiency of the Simple Groups of Order Less Than a Million and Their Covers

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Pages 347-358 | Published online: 30 Jan 2011

  • Wieb Bosma, John Cannon, and Catherine Playoust. "The Magma Algebra System I: The User Language." J. Symbolic Comput. 24 (1997), 235–265.
  • J. N. Bray, M. D. E. Conder, C. R. Leedham- Green, and E. A. O'Brien. "Short Presentations for Alternating and Symmetric Groups." Preprint, 2006.
  • C. M. Campbell and E. F. Robertson." A Deficiency Zero Presentation for SL(2, p)." Bull. London Math. Soc. 12 (1980), pp. 17–20.
  • C. M. Campbell and E. F. Robertson. "Presentations for the Simple Groups G, 105 < |G| < 106." Comm. Algebra 12 (1984), 2643–2663.
  • Colin M. Campbell and Edmund F. Robertson. "Computing with Finite Simple Groups and Their Covering Groups." In Computers in Algebra, edited by M. C. Tangora, 17–26. New York: Marcel Dekker, 1988.
  • C. M. Campbell, E. F. Robertson, T. Kawamata, I. Miyamoto, and P. D. Williams. "Deficiency Zero Presentations for Certain Perfect Groups." Proc. Roy. Soc. Edinburgh 103A (1986), 63–71.
  • Colin M. Campbell, E. F. Robertson, and P. D.Williams. "Efficient Presentations for Finite Simple Groups and Related Groups." In Groups-Korea 1988, pp. 65–72, Lecture Notes in Mathematics 1398. New York: Springer-Verlag, 1989.
  • C. M. Campbell, E. F. Robertson, and P. D. Williams. "On Presentations of PSL(2, pn)." J. Austral. Math. Soc. 48 (1990), 333–346.
  • Colin M. Campbell, George Havas, Alexander Hulpke, and Edmund F. Robertson. "Efficient Simple Groups." Comm. Algebra 31 (2003), 5191–5197.
  • Colin M. Campbell, George Havas, Colin Ramsay, and Edmund F. Robertson. "Nice Efficient Presentations for All Small Simple Groups and Their Covers." LMS J. Comput. Math. 7 (2004), 266–283.
  • Marston Conder, George Havas, and Colin Ramsay. "Efficient Presentations for the Mathieu Simple Group M22 and Its Cover." In Finite Geometries, Groups, and Computation, pp. 33–42. Berlin: Walter de Gruyter, 2006.
  • J. H. Conway, R. T. Curtis, S. P. Norton, R. A. Parker, and R. A. Wilson. Atlas of Finite Groups. Oxford: Oxford University Press, 1985.
  • D. B. A. Epstein. "Finite Presentations of Groups and 3-Manifolds." Quart. J. Math. Oxford Ser. (2) 12 (1961), 205–212.
  • Greg Gamble, Alexander Hulpke, George Havas, and Colin Ramsay. "GAP Package ACE; Advanced Coset Enumerator." Available online (http://www. gap-system.org/Packages/ace.html), 2004. http://www.gap-system.org/Packages/ace.html
  • The GAP Group. "GAP–Groups, Algorithms, and Programming, Version 4.4." Available online (http://www.gap-system.org/), 2004. http://www.gap-system.org/
  • The GAP Group. "Balanced Presentations for Covering Groups of Simple Groups." Available online (http://www.gap-system.org/Doc/Examples/ balanced.html), 2004. http://www.gap-system.org/Doc/Examples/balanced.html
  • R. M. Guralnick, W. M. Kantor, M. Kassabov, and A. Lubotzky. "Presentations of Finite Simple Groups: A Quantitative Approach." To appear in J. Amer. Math. Soc. Preprint, 2007.
  • R. M. Guralnick, W. M. Kantor, M. Kassabov, and A. Lubotzky. "Presentations of Finite Simple Groups: A Computational Approach." Preprint, 2007.
  • George Havas and Colin Ramsay. "Proving a Group Trivial Made Easy: A Case Study in Coset Enumeration." Bull. Austral. Math. Soc. 62 (2000), 105–118.
  • George Havas and Colin Ramsay. "Coset Enumeration: ACE Version 3.001." Available online (http://www.itee.uq.edu.au/~havas/ace3001.tar.gz), 2001. http://www.itee.uq.edu.au/~havas/ace3001.tar.gz
  • George Havas and Colin Ramsay. "Short Balanced Presentations of Perfect Groups." Groups St Andrews 2001 in Oxford, Volume 1, London Mathematical Society Lecture Note Series 304, pp. 238–243. Cambridge: Cambridge University Press, 2003.
  • George Havas and Colin Ramsay. "Breadth-First Search and the Andrews–Curtis Conjecture." Internat. J. Algebra Comput. 13 (2003), 61–68.
  • George Havas, M. F. Newman, and E. A. O'Brien. "On the Efficiency of Some Finite Groups." Comm. Algebra 32 (2004), 649–656.
  • A. Jamali and E. F. Robertson. "Efficient Presentations for Certain Simple Groups." Comm. Algebra 17 (1989), 2521–2528.
  • Inna Korchagina and Alexander Lubotzky. "On Presentations and Second Cohomology of Some Finite Simple Groups." Publ. Math. Debrecen 69 (2006), 341–352.
  • J. G. Sunday. "Presentations of the Groups SL(2,m) and PSL(2,m)." Canad. J. Math. 24 (1972), 1129–1131.
  • John S. Wilson. "Finite Axiomatization of Finite Soluble Groups." J. London Math. Soc. (2) 74 (2006), 566- 582.

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