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The Alperin Weight Conjecture and Uno's Conjecture for the Baby Monster B, p Odd

Published online by Cambridge University Press:  01 February 2010

Jianbei An  and
R. A. Wilson
Jianbei An
Affiliation:
Department of Mathematics, University of Auckland, Auckland, New Zealand, [email protected]
R. A. Wilson
Affiliation:
Department of Mathematics The University of BirminghamBirmingham B15 2TT United Kingdom, [email protected]

Abstract

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Suppose that p is 3, 5 or 7. In this paper, faithful permutation representations of maximal p-local subgroups are constructed, and the radical p-chains of the Baby Monster B are classified. Hence, the Alperin weight conjecture and the Uno reductive conjecture can be verified for B, the latter being a refinement of Dade's reductive conjecture and the Isaacs-Navarro conjecture.

Type
Research Article
Information
LMS Journal of Computation and Mathematics , Volume 7 , 2004 , pp. 120 - 166
Copyright
Copyright © London Mathematical Society 2004

References

1. Alperin, J. L., ‘Weights for finite groups’, The Arcata Conference on Representations of Finite Groups, Proc. Sympos. Pure Math. 47 (1987) 369–379.CrossRefGoogle Scholar
2. An, Jianbei, Eaton, C. W., ‘The p-local rank of a block’, J. Group Theory 3 (2000) 369–380.CrossRefGoogle Scholar
3. An, Jianbei, Eaton, C. W., ‘Modular representation theory of blocks with trivial intersection defect groups’, Algebr. Represent. Theory, to appear.Google Scholar
4. An, Jianbei, Brien, E.A.O', ‘A local strategy to decide the Alperin and Dade conjectures’, J. Algebra 206 (1998) 183–207.CrossRefGoogle Scholar
5. An, Jianbei, Brien, E.A.O', ‘The Alperin and Dade conjectures for the simple Fischer group Fi23’, International J. Algebra Comput. 9 (1999) 621–670.CrossRefGoogle Scholar
6. Bosma, Wieb, Cannon, John, Playoust, Catherine, ‘The MAGMA algebra system I: the user language’, J. Symbolic Comput. 24 (1997) 235–265.Google Scholar
7. Conway, J. H., Curtis, R. T., Norton, S. P., Parker, R. A., Wilson, R. A., Atlas of finite groups (Clarendon Press, Oxford, 1985).Google Scholar
8. Dade, E. C., ‘Counting characters in blocks Counting characters in blocks’, I, Invent. Math. 109 (1992) 187–210.CrossRefGoogle Scholar
9. Dade, E. C., ‘Counting characters in blocksCounting 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
10. The GAP Team, ‘GAP - Groups, Algorithms, and Programming’, Version 4. Lehrstuhl D für Mathematik, RWTH Aachen, and School of Mathematical and Computational Sciences, University of St Andrews (2000).Google Scholar
11. , G.Hiss, Lux, K., Brauer trees of sporadic groups (Oxford Science Publications, 1989).Google Scholar
12. Isaacs, I. M., Navarro, G., ‘New refinements of the McKay conjecture for arbitrary finite groups’, Ann of Math 156 (2002) 333–344.CrossRefGoogle Scholar
13. Knörr, R., ‘On the vertices of irreducible modules’, Ann. of Math. 110(1979) 487–499.CrossRefGoogle Scholar
14. Linton, S., Parker, R., Wilson, R., ‘Computer construction of the Monsters’, J. Group Theory 1 (1998) 307–337.Google Scholar
15. Uno, K., ‘Conjectures on character degrees for the simple Thompson group’, Osaka J. Math., to appear.Google Scholar
16. Wilson, Robert A., ‘Some subgroups of baby monster’, Invent. Math. 89 (1987) 197–218.CrossRefGoogle Scholar
17. Wilson, R. A. et al. , ‘ATLAS of finite group representations’, http://www.mat.bham.ac.uk/atlas.Google Scholar