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Completing the Brauer Trees for the Sporadic Simple Lyons Group

Published online by Cambridge University Press:  01 February 2010

Jürgen Müller ,
Max Neunhöffer ,
Frank Röhr  and
Robert Wilson
Jürgen Müller
Affiliation:
Lehrstuhl D für Mathematik, RWTH Aachen, Templergraben 64, D-52062 Aachen, Germany, mueller@math.rwth-aachen.de
Max Neunhöffer
Affiliation:
Lehrstuhl D für Mathematik, RWTH Aachen, Templergraben 64, D-52062 Aachen, Germany, max.neunhoeffer@math.rwth-aachen.de
Frank Röhr
Affiliation:
Institut für Informatik und Gesellschaft, Abteilung Modellbildung und soziale Folgen, Universität Freiburg, D-79085 Freiburg i.Br., Germany, roehr@modell.iig.uni-freiburg.de
Robert Wilson
Affiliation:
School of Mathematics and Statistics, The University of Birmingham, Edgbaston, Birmingham B15 2TT, R. A. Wilson@bham.ac.uk

Abstract

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In this paper, the Brauer trees are completed for the sporadic simple Lyons group Ly in characteristics 37 and 67. The results are obtained using tools from computational representation theory—in particular, a new condensation technique—and with the assistance of the computer algebra systems MeatAxe and GAP.

Type
Research Article
Information
LMS Journal of Computation and Mathematics , Volume 5 , 2002 , pp. 18 - 33
Copyright
Copyright © London Mathematical Society 2002

References

1Bray, J. ‘An improved method for generating the centraliser of an involution’, Arich.Math. 74 (2000) 241–245.CrossRefGoogle Scholar
2Breuer, T. et al. , ‘The modular atlas’, http://www.math.rwth-aachen.de/~moc.Google Scholar
3Conway, J., Curtis, R., Norton, S., Parker, R., Wilson, R., Atlas of finite groups (Clarendon Press, 1985).Google Scholar
4Cooperman, G., Hiss, G., Lux, K.Müller, J., ‘The Brauer tree of the principal 19-block of the sporadic simple Thompson group’, Experiment. Math. 6 (1997) 293–300.CrossRefGoogle Scholar
5Feit, W., The representation theory of finite groups (North-Holland, 1982).Google Scholar
6The Gap Group, Gap —Groups, Algorithms, and Programming, Version 4.2 (Aachen/St. Andrews, 2000); http://www.gap-system.org/.Google Scholar
7Green, J., Polynomial representations of GLn, Lecture Notes in Math. 830 (Springer,1980).Google Scholar
8Hiss, G., Lux, K., Brauer trees of sporadic groups (Clarendon Press, 1989).Google Scholar
9Jansen, C., Wilson, R., ‘The minimal faithful 3-modular representation of the Lyons group’, Comm. Algebra 24 (1996) 873–879.CrossRefGoogle Scholar
10Jansen, C., Lux, K.Parker, R.Wilson, R., An atlas of Brauer characters (Claren don Press, 1995).Google Scholar
11Lübeck, F., ‘Conway ploynomials of finite fields’; http://www.math.rwth-aachen.de/~Frank.Luebeck/ConwayPol/Google Scholar
12Lübeck, F., Neunhöffer, M., ‘Enumerating large orbits and direct condensation’, Experiment. Math. 10 (2001) 197–205.Google Scholar
13Lux, K., Müller, J., Ringe, M.,‘Peakword condensation and submodule lattices:an application of the MeatAxe’, J. Symb. Comp. 17 (1994) 529–544.Google Scholar
14Meyer, W., Neutsch, W., Parker, R., ‘The minimal 5-representation of Lyons sporadic group’, Math. Ann. 272 (1985) 29–39.CrossRefGoogle Scholar
15Ottensmann, M., ‘Vervollständigung der Brauer-Bäume von 3.ON in Charakteristik 11, 19 und 31 mit Methoden der Kondensation’, Diplomarbeit, Lehrstuhl D für Mathematik, RWTH Aachen, 2000.Google Scholar
16Parker, R., Wilson, R., ‘Constructions of Fischer's Baby Monster over fields of characteristic not 2’, J. Algebra 229 (2000) 109–117.CrossRefGoogle Scholar
17Ringe, M., The C-MeatAxe Manual, Version 2.4 (Lehrstuhl D für Mathematik, RWTH Aachen, 2000).Google Scholar
18Röhr, F., ‘Die Brauer-Charaktere der sporadischen einfachen Rudvalis-Gruppe in Charakteristik 13 und 29’, Diplomarbeit, Lehrstuhl D für Mathematik, RWTH Aachen, 2000.Google Scholar
19Thackray, J., ‘Modular representations of some finite groups’, PhD thesis, Cambridge University, 1981.Google Scholar
20Wilson, R., ‘Standard generators for sporadic simple groups’, J. Algebra 184 (1996) 505–515.CrossRefGoogle Scholar
21Wilson, R. et al. , ‘Atlas of finite group representations’, http://www.mat.bham.ac.uk/atlas/.Google Scholar