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Involutions in Janko’s simple group J4

Part of: Representation theory of groups

Published online by Cambridge University Press:  01 November 2011

Peter Rowley  and
Paul Taylor
Peter Rowley
Affiliation:
School of Mathematics, University of Manchester, Oxford Road, Manchester, M13 9PL, United Kingdom (email: peter.j.rowley@manchester.ac.uk)
Paul Taylor
Affiliation:
School of Mathematics, University of Manchester, Oxford Road, Manchester, M13 9PL, United Kingdom (email: p.taylor@maths.manchester.ac.uk)

Abstract

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In this paper we determine the suborbits of Janko’s largest simple group in its conjugation action on each of its two conjugacy classes of involutions. We also provide matrix representatives of these suborbits in an accompanying computer file. These representatives are used to investigate a commuting involution graph for J4.

Supplementary materials are available with this article.

MSC classification

Secondary: 20D08: Simple groups
Type
Research Article
Information
LMS Journal of Computation and Mathematics , Volume 14 , 2011 , pp. 238 - 253
Copyright
Copyright © London Mathematical Society 2011

References

[1]Bates, C., Bundy, D., Perkins, S. and Rowley, P., ‘Commuting involution graphs for sporadic groups’, J. Algebra 316 (2007) 849–868.CrossRefGoogle Scholar
[2]Bates, C. and Rowley, P., ‘Involutions in Conway’s largest simple group’, LMS J. Comput. Math. 7 (2004) 337–351.CrossRefGoogle Scholar
[3]Bates, C., Rowley, P. and Taylor, P., ‘Involutions in the automorphism group of small sporadic groups’, MIMS Eprint 2011.67, Manchester Institute for Mathematical Sciences, The University of Manchester, http://eprints.ma.man.ac.uk/1660/.Google Scholar
[4]Bates, C. and Rowley, P., ‘Centralizers of real elements in finite groups’, Arch. Math. 85 (2005) 485–489.CrossRefGoogle Scholar
[5]Bosma, W., Cannon, J. and Playoust, C., ‘The Magma algebra system I: the user language’, J. Symbolic Comput. 24 (1997) 235–265.CrossRefGoogle Scholar
[6]Brauer, R. and Fowler, K. A., ‘On groups of even order’, Ann. of Math. (2) 62 (1955) 565–583.CrossRefGoogle Scholar
[7]Bray, J., ‘An improved method for generating the centralizer of an involution’, Arch. Math. 74 (2000) 241–245.CrossRefGoogle Scholar
[8]Conway, J. H., Curtis, R. T., Norton, S. P., Parker, R. A. and Wilson, R. A., Atlas of finite groups (Clarendon, Oxford, 1985).Google Scholar
[9] The GAP group, ‘GAP—groups, algorithms, and programming, version 4.3’, 2002, http://www.gap-system.org.Google Scholar
[10]Ivanov, A. A. and Meierfrankenfeld, U., ‘A computer-free construction of J 4’, J. Algebra 219 (1999) no. 1, 113–172.CrossRefGoogle Scholar
[11]Janko, Z., ‘A new finite simple group of order 86,775,571,046,077,562,880 which possesses M 24 and the full covering group of M 22 as subgroups’, J. Algebra 42 (1976) no. 2, 564–596.CrossRefGoogle Scholar
[12]Kleidman, P. B. and Wilson, R. A., ‘The maximal subgroups of J 4’, Proc. Lond. Math. Soc. (3) 56 (1988) no. 3, 484–510.CrossRefGoogle Scholar
[13]Lempken, W., ‘Die Untergruppenstruktur der endlichen, einfachen Gruppe J 4’, Thesis, Mainz, 1985.Google Scholar
[14]Lempken, W., ‘On local and maximal subgroups of Janko’s simple group J 4’, Rend. Accad. Naz. Sci. XL Mem. Mat. (5) 13 (1989) no. 1, 47–103.Google Scholar
[15]Norton, S., ‘The construction of J 4’, The Santa Cruz conference on finite groups (University of California, Santa Cruz, CA, 1979), Proceedings of Symposia in Pure Mathematics 37 (American Mathematical Society, Providence, RI, 1980) 271–277.Google Scholar
[16]Parker, R. A., ‘The computer calculation of modular characters (the Meat-axe)’, Computational group theory (Durham, 1982) (Academic Press, London, 1984) 267–274.Google Scholar
[17]Rowley, P. and Taylor, P., ‘Point–line collinearity graphs of two sporadic minimal parabolic geometries’, J. Algebra 331 (2011) no. 1, 301–310.CrossRefGoogle Scholar
[18]Taylor, P., ‘Involutions in the Fischer groups’, MIMS Eprint 2011.41, Manchester Institute for Mathematical Sciences, The University of Manchester, http://eprints.ma.man.ac.uk/1622/.Google Scholar
[19]Wilson, R., Walsh, P., Tripp, J., Suleiman, I., Rogers, S., Parker, R., Norton, S., Linton, S. and Bray, J., ‘Atlas of finite group representations’, http://brauer.maths.qmul.ac.uk/Atlas/v3/.Google Scholar
Supplementary material: File

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