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The Alperin Weight Conjecture and Dade's Conjecture for the Simple Group J4

Published online by Cambridge University Press:  01 February 2010

Jianbei An ,
E. A. O'Brien  and
R. A. Wilson
Jianbei An
Affiliation:
Department of Mathematics, University of Auckland, Auckland, New Zealandan@math.auckland.ac.nz
E. A. O'Brien
Affiliation:
Department of Mathematics, University of Auckland, Auckland, New Zealandobrien@math.auckland.ac.nz
R. A. Wilson
Affiliation:
Department of Mathematics, The University of Birmingham, Birmingham B15 2TTR.A.Wilson@bham.ac.uk

Abstract

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The authors construct faithful permutation representations of maximal 2-local subgroups and classify the radical chains of the Janko simple group J4; hence the Alperin weight conjecture and the Dade reductive conjecture for J4 are verified.

Type
Research Article
Information
LMS Journal of Computation and Mathematics , Volume 6 , 2003 , pp. 119 - 140
Copyright
Copyright © London Mathematical Society 2003

References

1Alperin, J.L., ‘Weights for finite groups‘, The Arcata Conference on Representations of Finite Groups, Proc. Sympos. Pure Math. 47 (Amer. Math. Soc, Providence, RI, 1987)369–379.CrossRefGoogle Scholar
2An, Jianbei and Eaton, C.W., ‘The p-local rank of a block’, J. Group Theory 3 (2000) 369–.CrossRefGoogle Scholar
3An, Jianbei and O'Brien, E.A., A local strategy to decide the Alperin and Dade conjectures’, J. Algebra 206 (1998) 183–207.CrossRefGoogle Scholar
4An, Jianbei and O'Brien, E.A., ‘The Alperin and Dade conjectures for the simple Fischer group Fi23’, Internal J. Algebra Comput. 9 (1999) 621–670.CrossRefGoogle Scholar
5Wilson, A. et al. , ‘ATLAS of finite group representations’, http://www.mat.bham.ac.uk/atlas.Google Scholar
6Blau, H.I. and Michler, G.O., ‘Modular representation theory of finite groups with T. I. Sylow p-subgroups’, Trans. Amer. Math. Soc. 319 (1990) 417–68.Google Scholar
7Bosma, Wieb, Canon, John and Playoust, Catherine, ‘The MAGMA algebra system I: The user language’, J. Symbolic Comput. 24 (1997) 235–265.CrossRefGoogle Scholar
8Conway, J.H., Curtis, R.T., Norton, S.P., Parker, R.A. and Wilson, R.A., Atlas of finite groups (Clarendon Press, Oxford, 1985).Google Scholar
9Dade, E.C., ‘Counting characters in blocks, I’;, Invent. Math. 109 (1992) 187–210.CrossRefGoogle Scholar
10Dade, E.C., ‘Counting characters in blocks,II.9’, Representation theory of finite groups (Columbus, OH, 1995), Ohio State Univ. Math. Res. Inst. Publ. 6 (de Gruyter, Berlin, 1997)45–59.Google Scholar
11Eaton, C.W., ‘On finite groups of p-local rank one and conjectures of Dade and Robinson’, J. Algebra 238 (2001) 623–642.CrossRefGoogle Scholar
12THE GAP GROUP, ‘GAP - groups, algorithms, and programming, Version 4.3’ (2002), http://www.gap-system.org.Google Scholar
13Hiss, G. and Lux, K., Brauer trees of sporadic groups (Oxford Science Publications, 1989).Google Scholar
14Kleidman, P.B. and Wilson, R.A., ‘The maximal subgroups of J4’, Proc. London Math. Soc. 56 (1988) 484–510.CrossRefGoogle Scholar
15Nagao, H. and Tsushima, Y., Representations of finite groups, (Academic Press, Inc., Boston, MA, 1989).Google Scholar
16Wilson, Robert A., ‘Standard generators for sporadic simple groups’, J. Algebra 184 (1996) 505–515.CrossRefGoogle Scholar
17Yoshiara, Satoshi, ‘The radical 2-subgroups of the sporadic simple groups J4, C02 and Th’, J. Algebra 233 (2000) 309–341.CrossRefGoogle Scholar