Abstract
We give a presentation of the Lyons simple group together with information on a complete computational proof that the presentation is correct. This fills a longstanding gap in the literature on the sporadic simple groups. This presentation is a basis for various matrix and permutation representations of the group.
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W. Bosma, J. Cannon and C. Playoust: The Magma algebra system I: The user language, J. Symbolic Comput. 24, (1997) 235–265. http://www.maths.usyd.edu.au:8000/comp/magma/Overview.html
G. Cooperman and G. Havas: Practical parallel coset enumeration, in: Workshop on High Performance Computing and Gigabit Local Area Networks, Lecture Notes in Control and Information Systems 226, (1997) 15–27.
L.E. Dickson: Theory of linear groups in an arbitrary field,Trans. Amer. Math. Soc. 2, (1901) 363–394.
L.E. Dickson: A new system of simple groups, Math. Ann. 60, (1905) 137–150.
H.W. Gollan: A new existence proof for Ly, the sporadic simple group of R. Lyons, Preprint 30, Institut für Experimentelle Mathematik, Universität GH Essen, 1995.
H.W. Gollan and G. Havas: On Sims’ presentation for Lyons’ simple group, These proceedings, chapter 13.
G. Havas: Coset enumeration strategies, in: ISSAC’91, Proc. 1991 Internat. Sympos. Symbolic and Algebraic Computation (ACM Press, New York, 1991) 191–199.
C. Jansen and R.A. Wilson: The minimal faithful 3-modular representation for the Lyons group, Commun Algebra 24, (1996) 873–879.
R. Lyons: Evidence for a new finite simple group, J. Algebra 20, (1972) 540–569.
R. Lyons: Evidence for a new finite simple group, (Errata) J. Algebra 34, (1975) 188–189.
W. Meyer, W. Neutsch and R. Parker: The minimal 5-representation of Lyons’ sporadic group, Math. Ann. 272 (1985) 29–39.
M. Schönert et al.: GAP - Groups, Algorithms and Programming, (Lehrstuhl D für Mathematik, Rheinisch-Westfälische Technische Hochschule, Aachen, Germany, fifth edition, 1995).http://www.groups.dcs.st.and.ac.uk/~gap
C.C. Sims: The existence and uniqueness of Lyons’group,in: Finite Groups’72 (North Holland, 1973) 138–141
C.C. Sims: Computation with finitely presented groups, Cambridge University Press (1994).
R.A. Wilson: A representation for the Lyons group in GL 2480(4), and a new uniqueness proof, Arch. Math. 70,(1998) 11–15.
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Havas, G., Sims, C.C. (1999). A Presentation for the Lyons Simple Group. In: Dräxler, P., Ringel, C.M., Michler, G.O. (eds) Computational Methods for Representations of Groups and Algebras. Progress in Mathematics, vol 173. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8716-8_14
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DOI: https://doi.org/10.1007/978-3-0348-8716-8_14
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-9740-2
Online ISBN: 978-3-0348-8716-8
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