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VARIATIONS ON THOMPSON'S CHARACTER DEGREE THEOREM

Published online by Cambridge University Press:  26 February 2003

Gabriel Navarro  and
Thomas Wolf
Gabriel Navarro
Affiliation:
Departament d' Algebra, Facultat de Matematiques, Universitat de Valencia, 46100 Burjassot, Valencia, Spain email: gabriel@uv.es
Thomas Wolf
Affiliation:
Department of Mathematics, Ohio University, Athens, OH 45701, USA email: wolf@ohiou.edu
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If P is a Sylow-p-subgroup of a finite p-solvable group G, we prove that G^\prime \cap \bf{N}_G(P) \subseteq {P} if and only if p divides the degree of every irreducible non-linear p-Brauer character of G. More generally if π is a set of primes containing p and G is π-separable, we give necessary and sufficient group theoretic conditions for the degree of every irreducible non-linear p-Brauer character to be divisible by some prime in π. This can also be applied to degrees of ordinary characters.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 44 , Issue 3 , September 2002 , pp. 371 - 374
Copyright
2001 Glasgow Mathematical Journal Trust