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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

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