Dimensions of irreducible modules over twisted group algebras |
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Authors: | G Karpilovsky |
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Institution: | (1) Present address: Department of Mathematics, University of the Witwatersrand, 1 Jan Smuts Avenue, 2001 Johannesburg, South Africa |
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Abstract: | LetN be a normal subgroup of a finite groupG, letF be an algebraically closed field, let![agr](/content/lph7563558100634/xxlarge945.gif) Z
2(G, F
*) and letV be an irreducible module over the twisted group algebraF
. If charF=p>0 divides (G N), assume thatG/N isp-solvable. It is proved that dim
F
V divides (G N)d whered is the dimension of an irreducible constituent ofV
N. The special case where =1 andN is abelian yields a well-known theorem of Dade 3]. Another special case, namely whereN is abelian, charF (G N) and the restriction of ofNxN is a coboundary is a generalization of the main result of Ng 5]. |
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Keywords: | |
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