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On the degree of an indecomposable representation of a finite group

Part of: Representation theory of groups

Published online by Cambridge University Press:  09 April 2009

Gerald H. Cliff
Gerald H. Cliff
Affiliation:
Department of Mathematics University of AlbertaEdmonton, Alberta, Canada
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Abstract

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Let k be an algebraically closed field of characteristic p, and G a finite group. Let M be an indecomposable kG-module with vertex V and source X, and let P be a Sylow p-subgroup of G containing V. Theorem: If dimkX is prime to p and if NG(V) is p-solvable, then the p-part of dimkM equals [P:V]; dimkX is prime to p if V is cyclic.

MSC classification

Secondary: 20C20: Modular representations and characters
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 28 , Issue 3 , November 1979 , pp. 321 - 324
Copyright
Copyright © Australian Mathematical Society 1979

References

Conlon, S. B. (1964), ‘Twisted group algebras and their representations’, J. Austral. Math. Soc. 4, 152–173.CrossRefGoogle Scholar
Curtis, C. W. and Reiner, I. (1962), Representation theory of finite groups and associative algebras (Interscience, New York).Google Scholar
Green, J. A. (1959), ‘On the indecomposable representations of a finite group’, Math. Z. 70, 430–445.CrossRefGoogle Scholar
Green, J. A. (1964), ‘A transfer theorem for modular representations’, J. Algebra 1, 73–84.CrossRefGoogle Scholar
Tucker, P. A. (1965), ‘On the reduction of induced indecomposable representations’, Amer. J. Math. 87, 798–806.CrossRefGoogle Scholar