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Cliques of Irreducible Representations, Quotient Groups, and Brauer's Theorems on Blocks

Published online by Cambridge University Press:  20 November 2018

Harald Ellers
Harald Ellers*
Affiliation:
Department of Mathematics, Northern Illinois University, DeKalb, Illinois 60115, U.S.A. e-mail: [email protected]
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Abstract

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Assume k is an algebraically closed field of characteristic p and G is a finite group. If P is a p-subgroup of G such that G = PCG(P), and if H is a normal subgroup of G with P ≤ H, then the number of H-cliques of irreducible k[G]-modules is the same as the number of H/P-cliques of irreducible k[G/P]-modules.

Keywords

20C20
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 47 , Issue 5 , 01 October 1995 , pp. 929 - 945
Copyright
Copyright © Canadian Mathematical Society 1995

References

1. Alperin, J.L., Weights for finite groups. In: The Areata conference on representations of finite groups, Proceedings of Symposia in Pure Mathematics 47, part 1, (ed. Paul Fong), Amer. Math. Soc, Providence, 1986.Google Scholar
2. Brown, K.S., Cohomology of groups, Springer-Verlag, New York, 1982.Google Scholar
3. Conlon, S.B., Twisted group algebras and their representations, J. Austral. Math. Soc. 4(1964), 152–173.Google Scholar
4. Curtis, C.W. and Reiner, I., Methods of representation theory, vol. 2, Wiley-Interscience, New York, 1987.Google Scholar
5. Dade, E.C., Compounding Clifford's theory, Ann. of Math. (2) 91(1970), 263–290.Google Scholar
6. Dade, E.C., Isomorphisms of Clifford extensions, Ann. of Math. (2) 92(1970), 375–433.Google Scholar
7. Dade, E.C., Block extensions, Illinois J. Math. 17(1973), 198–272.Google Scholar
8. Dade, E.C., The equivalence of various generalizations of group rings and modules, Math. Z. 181(1982), 335–344.Google Scholar
9. Ellers, H., Cliques of irreducible representations of p-solvable groups and a theorem analogous to Alperin s conjecture, Math. Z. 217(1994), 607–634.Google Scholar
10. Ellers, H., The defect groups of a clique, p-solvable groups, and Alperin's conjecture, J. Reine Angew. Math., to appear.Google Scholar
11. Feit, W., The representation theory of finite groups, North-Holland, Amsterdam, 1982.Google Scholar
12. Gorenstien, D., Finite groups, Harper and Row, New York, 1968.Google Scholar
13. Maclane, S., Homology, Springer-Verlag, Heidelberg, 1963.Google Scholar