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Involutions in Janko’s simple group J4

  • Peter Rowley (a1) and Paul Taylor (a2)

Abstract

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.

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References

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[1]Bates, C., Bundy, D., Perkins, S. and Rowley, P., ‘Commuting involution graphs for sporadic groups’, J. Algebra 316 (2007) 849868.
[2]Bates, C. and Rowley, P., ‘Involutions in Conway’s largest simple group’, LMS J. Comput. Math. 7 (2004) 337351.
[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/.
[4]Bates, C. and Rowley, P., ‘Centralizers of real elements in finite groups’, Arch. Math. 85 (2005) 485489.
[5]Bosma, W., Cannon, J. and Playoust, C., ‘The Magma algebra system I: the user language’, J. Symbolic Comput. 24 (1997) 235265.
[6]Brauer, R. and Fowler, K. A., ‘On groups of even order’, Ann. of Math. (2) 62 (1955) 565583.
[7]Bray, J., ‘An improved method for generating the centralizer of an involution’, Arch. Math. 74 (2000) 241245.
[8]Conway, J. H., Curtis, R. T., Norton, S. P., Parker, R. A. and Wilson, R. A., Atlas of finite groups (Clarendon, Oxford, 1985).
[9] The GAP group, ‘GAP—groups, algorithms, and programming, version 4.3’, 2002, http://www.gap-system.org.
[10]Ivanov, A. A. and Meierfrankenfeld, U., ‘A computer-free construction of J 4’, J. Algebra 219 (1999) no. 1, 113172.
[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, 564596.
[12]Kleidman, P. B. and Wilson, R. A., ‘The maximal subgroups of J 4’, Proc. Lond. Math. Soc. (3) 56 (1988) no. 3, 484510.
[13]Lempken, W., ‘Die Untergruppenstruktur der endlichen, einfachen Gruppe J 4’, Thesis, Mainz, 1985.
[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, 47103.
[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) 271277.
[16]Parker, R. A., ‘The computer calculation of modular characters (the Meat-axe)’, Computational group theory (Durham, 1982) (Academic Press, London, 1984) 267274.
[17]Rowley, P. and Taylor, P., ‘Point–line collinearity graphs of two sporadic minimal parabolic geometries’, J. Algebra 331 (2011) no. 1, 301310.
[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/.
[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/.
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