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Real class sizes and real character degrees

Published online by Cambridge University Press:  22 June 2010

ROBERT M. GURALNICK ,
GABRIEL NAVARRO  and
PHAM HUU TIEP
ROBERT M. GURALNICK
Affiliation:
Department of Mathematics, University of Southern California, Los Angeles, CA 90089-2532, U.S.A. e-mail: guralnic@math.usc.edu
GABRIEL NAVARRO
Affiliation:
Departament d'Àlgebra, Universitat de València, 46100 Burjassot, València, Spain. e-mail: gabriel@uv.es
PHAM HUU TIEP
Affiliation:
Department of Mathematics, University of Arizona, Tucson, AZ 32611-0089, U.S.A. e-mail: tiep@math.arizona.edu
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Extract

Perhaps unexpectedly, there is a rich and deep connection between field of values of characters, their degrees and the structure of a finite group. Some of the fundamental results on the degrees of characters of finite groups, as the Ito–Michler and Thompson's theorems, admit a version involving only characters with certain fixed field of values ([DNT, NS, NST2, NT1, NT3]).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 150 , Issue 1 , January 2011 , pp. 47 - 71
Copyright
Copyright © Cambridge Philosophical Society 2010

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