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Irreducible characters of even degree and normal Sylow 2-subgroups

Published online by Cambridge University Press:  15 July 2016

NGUYEN NGOC HUNG  and
PHAM HUU TIEP
NGUYEN NGOC HUNG
Affiliation:
Department of Mathematics, The University of Akron, Akron, Ohio 44325, U.S.A. e-mail: hungnguyen@uakron.edu
PHAM HUU TIEP
Affiliation:
Department of Mathematics, University of Arizona, Tucson, Arizona 85721, U.S.A. e-mail: tiep@math.arizona.edu
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Abstract

The classical Itô-Michler theorem on character degrees of finite groups asserts that if the degree of every complex irreducible character of a finite group G is coprime to a given prime p, then G has a normal Sylow p-subgroup. We propose a new direction to generalize this theorem by introducing an invariant concerning character degrees. We show that if the average degree of linear and even-degree irreducible characters of G is less than 4/3 then G has a normal Sylow 2-subgroup, as well as corresponding analogues for real-valued characters and strongly real characters. These results improve on several earlier results concerning the Itô-Michler theorem.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 162 , Issue 2 , March 2017 , pp. 353 - 365
Copyright
Copyright © Cambridge Philosophical Society 2016 

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