Table of Contents
Algebra
Volume 2015 (2015), Article ID 587629, 15 pages
http://dx.doi.org/10.1155/2015/587629
Research Article

Involutions in the Automorphism Groups of Small Sporadic Simple Groups

School of Mathematics, The University of Manchester, Alan Turing Building, Oxford Road, Manchester M13 6PL, UK

Received 31 July 2014; Accepted 26 November 2014

Academic Editor: Peter Fleischmann

Copyright © 2015 Chris Bates et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. R. H. Bing, “A homeomorphism between the 3-sphere and the sum of two solid horned spheres,” Annals of Mathematics: Second Series, vol. 56, pp. 354–362, 1952. View at Publisher · View at Google Scholar · View at MathSciNet
  2. D. Montgomery and L. Zippin, “Examples of transformation groups,” Proceedings of the American Mathematical Society, vol. 5, pp. 460–465, 1954. View at Publisher · View at Google Scholar · View at MathSciNet
  3. J. W. Morgan and H. Bass, Eds., The Smith Conjecture, vol. 112 of Pure and Applied Mathematics, Academic Press, Orlando, Fla, USA, 1984, Papers presented at the symposium held at Columbia University, New York, NY, USA, 1979.
  4. C. M. Edwards and G. T. Rüttimann, “Involutive and Peirce gradings in JBW-triples,” Communications in Algebra, vol. 31, no. 6, pp. 2819–2848, 2003. View at Google Scholar
  5. J. Gornicki and B. E. Rhoades, “A general fixed point theorem for involutions,” Indian Journal of Pure and Applied Mathematics, vol. 27, no. 1, pp. 13–23, 1996. View at Google Scholar · View at MathSciNet · View at Scopus
  6. S. Montgomery, Fixed Rings of Finite Automorphism Groups of Associative Rings, vol. 818 of Lecture Notes in Mathematics, Springer, Berlin, Germany, 1980.
  7. T. A. Springer, “The classification of involutions of simple algebraic groups,” Journal of the Faculty of Science. University of Tokyo. Section IA. Mathematics, vol. 34, no. 3, pp. 655–670, 1987. View at Google Scholar · View at MathSciNet
  8. T. A. Springer, “Some results on algebraic group s with involutions,” in Algebraic Groups and Related Topics (Kyoto/Nagoya, 1983), vol. 6 of Advanced Studies in Pure Mathematics, pp. 525–543, North-Holland, Amsterdam, The Netherlands, 1985. View at Google Scholar
  9. W. Feit and J. G. Thompson, “Solvability of groups of odd order,” Pacific Journal of Mathematics, vol. 13, pp. 775–1029, 1963. View at Publisher · View at Google Scholar · View at MathSciNet
  10. R. Brauer and K. A. Fowler, “On groups of even order,” Annals of Mathematics, vol. 62, no. 3, pp. 565–583, 1955. View at Publisher · View at Google Scholar · View at MathSciNet
  11. D. Gorenstein, The Classification of Finite Ssimple Groups. Vol. 1, Groups of Noncharacteristic 2 Type. The University Series in Mathematics, Plenum Press, New York, NY, USA, 1983. View at Publisher · View at Google Scholar · View at MathSciNet
  12. D. Gorenstein, R. Lyons, and R. Solomon, The Classification of the Finite Simple Groups, vol. 40 of Mathematical Surveys and Monographs, American Mathematical Society, Providence, RI, USA, 1994.
  13. C. Bates and P. Rowley, “Involutions in Conway's largest simple group,” LMS Journal of Computation and Mathematics, vol. 7, pp. 337–351, 2004. View at Publisher · View at Google Scholar · View at MathSciNet
  14. P. Rowley and P. Taylor, “Point-line collinearity graphs of two sporadic minimal parabolic geometries,” Journal of Algebra, vol. 331, pp. 304–310, 2011. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  15. P. Rowley and P. Taylor, “Involutions in Janko's simple group J4,” LMS Journal of Computation and Mathematics, vol. 14, pp. 238–253, 2011. View at Publisher · View at Google Scholar · View at MathSciNet
  16. P. Taylor, “Involutions in Fischer's sporadic groups,” preprint, http://eprints.ma.man.ac.uk/1622.
  17. The GAP Group, GAP-Groups, Algorithms, Programming, Version 4.3, 2002, http://www.gap-system.org.
  18. W. Bosma, J. Cannon, and C. Playoust, “The Magma algebra system. I. The user language,” Journal of Symbolic Computation, vol. 24, no. 3-4, pp. 235–265, 1997. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  19. R. Wilson, P. Walsh, J. Tripp et al., “Atlas o f finite group representations,” http://brauer.maths.qmul.ac.uk/Atlas/v3.
  20. J. H. Conway, R. T. Curtis, S. P. Norton, R. A. Parker, and R. A. Wilson, Atlas of Finite Groups, Clarendon, Oxford, UK, 1985.
  21. R. A. Wilson, “Standard generators for sporadic simple groups,” Journal of Algebra, vol. 184, no. 2, pp. 505–515, 1996. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  22. D. Gorenstein, Finite Groups, Chelsea Publishing, New York, NY, USA, 2nd edition, 1980. View at MathSciNet