62
Views
2
CrossRef citations to date
0
Altmetric
Original Articles

Symmetric generation of M22

&
Pages 4257-4274 | Received 09 May 2016, Published online: 10 Feb 2017

References

  • Bradley, J. D., Curtis, R. T. (2006). Symmetric generation and existence of J3:2, the automorphism group of the third Janko group. J. Algebra 304(1):256–270.
  • Bradley, J. D., Curtis, R. T. (2010). Symmetric generation and existence of McL:2, the automorphism group of the McLaughlin group. Commun. Algebra 38(2):601–617.
  • Bray, J. N., Curtis, R. T. (2010). The Leech lattice Λ and the Conway group ⋅O revisited. Trans. Am. Math. Soc. 362(3):1351–1369.
  • Conway, J. H., Curtis, R. T., Norton, S. P., Parker, R. A., Wilson, R. A. (1985). Atlas of Finite Groups: Maximal Subgroups and Ordinary Characters for Simple Groups. Eynsham: Oxford University Press.
  • Curtis, R. T., Fairbairn, B. T. (2009). Symmetric representation of the elements of the Conway group ⋅0. J. Symbolic Comput. 44(8):1044–1067.
  • Curtis, R. T., Hasan, Z. (1996). Symmetric representation of the elements of the Janko group J1. J. Symbolic Comput. 22(2):201–214.
  • Curtis, R. T. (1976). A new combinatorial approach to M24. Math. Proc. Cambridge Philos. Soc. 79(1):25–42.
  • Curtis, R. T. (1992). Symmetric presentations. I. Introduction, with particular reference to the Mathieu groups M12 and M24. In: Groups, Combinatorics & Geometry (Durham, 1990). London Mathematical Society Lecture Note Series, Vol. 165. Cambridge: Cambridge University Press, pp. 380–396.
  • Curtis, R. T. (1993). Symmetric presentations. II. The Janko group J1. J. London Math. Soc. (2) 47(2):294–308.
  • Curtis, R. T. (2007). Symmetric Generation of Groups. Encyclopedia of Mathematics and its Applications. Vol. 111. Cambridge: Cambridge University Press (With applications to many of the sporadic finite simple groups).
  • Fairbairn, B. (2011). Recent progress in the symmetric generation of groups. In Groups St Andrews 2009 in Bath. Volume 2. London Mathematical Society Lecture Note Series, Vol. 388 Cambridge: Cambridge University Press, pp. 384–394.
  • Fairbairn, B. (2011). Symmetric presentations of Coxeter groups. Proc. Edinb. Math. Soc. (2) 54(3):669–683.
  • Iwasawa, K. (1941). Über die endlichen Gruppen und die Verbände ihrer Untergruppen. J. Fac. Sci. Imp. Univ. Tokyo. Sect. I. 4:171–199.
  • Mathieu, E. (1861). Memoire sur létude des fonctions de plusieurs quantités sur la manieére de les former et sur les substitutions qui les laissent invariable. Liouville J. (2) 18:241–323.
  • Mathieu, E. (1873). Sur la fonction cinq fois transitive de 24 quantités. Liouville J. (2) 18:25–47.
  • Parrott, D. (1970). On the Mathieu groups M22 and M11. J. Austral. Math. Soc. 11:69–81.
  • Wiedorn, C. (2003). A symmetric presentation for J1. Commun. Algebra 31(3):1329–1357.
  • Wilson, R. A. (2009). The Finite Simple Groups. Graduate Texts in Mathematics, Vol. 251. London: Springer-Verlag London, Ltd.
  • Witt, E. (1937). Die 5-fach transitiven gruppen von mathieu. Abh. Math. Semin. Univ. Hamburg 12(1):256–264.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.