Irreducible characters of even degree and normal Sylow 2-subgroups

Nguyen Ngoc Hung, Pham Huu Tiep

Research output: Contribution to journalArticlepeer-review

4 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)353-365
Number of pages13
JournalMathematical Proceedings of the Cambridge Philosophical Society
Volume162
Issue number2
DOIs
StatePublished - Mar 1 2017

ASJC Scopus subject areas

  • Mathematics(all)

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