The average character degree and an improvement of the Itô-Michler theorem

Nguyen Ngoc Hung; Pham Huu Tiep

doi:10.1016/j.jalgebra.2019.12.022

The average character degree and an improvement of the Itô-Michler theorem

Nguyen Ngoc Hung
, Pham Huu Tiep

Mathematics

Research output: Contribution to journal › Article › peer-review

7 Scopus citations

Abstract

The classical Itô-Michler theorem states that the degree of every ordinary irreducible character of a finite group G is coprime to a prime p if and only if the Sylow p-subgroups of G are abelian and normal. In an earlier paper [8], we used the notion of average character degree to prove an improvement of this theorem for the prime p=2. In this follow-up paper, we obtain a full improvement for all primes.

Original language	English (US)
Pages (from-to)	86-107
Number of pages	22
Journal	Journal of Algebra
Volume	550
DOIs	https://doi.org/10.1016/j.jalgebra.2019.12.022
State	Published - May 15 2020

Keywords

Character degrees
Finite groups
Itô-Michler theorem
Normal subgroups
Simple groups
Sylow subgroups

ASJC Scopus subject areas

Algebra and Number Theory

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10.1016/j.jalgebra.2019.12.022

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abstract = "The classical It{\^o}-Michler theorem states that the degree of every ordinary irreducible character of a finite group G is coprime to a prime p if and only if the Sylow p-subgroups of G are abelian and normal. In an earlier paper [8], we used the notion of average character degree to prove an improvement of this theorem for the prime p=2. In this follow-up paper, we obtain a full improvement for all primes.",

keywords = "Character degrees, Finite groups, It{\^o}-Michler theorem, Normal subgroups, Simple groups, Sylow subgroups",

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AU - Tiep, Pham Huu

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N2 - The classical Itô-Michler theorem states that the degree of every ordinary irreducible character of a finite group G is coprime to a prime p if and only if the Sylow p-subgroups of G are abelian and normal. In an earlier paper [8], we used the notion of average character degree to prove an improvement of this theorem for the prime p=2. In this follow-up paper, we obtain a full improvement for all primes.

AB - The classical Itô-Michler theorem states that the degree of every ordinary irreducible character of a finite group G is coprime to a prime p if and only if the Sylow p-subgroups of G are abelian and normal. In an earlier paper [8], we used the notion of average character degree to prove an improvement of this theorem for the prime p=2. In this follow-up paper, we obtain a full improvement for all primes.

KW - Character degrees

KW - Finite groups

KW - Itô-Michler theorem

KW - Normal subgroups

KW - Simple groups

KW - Sylow subgroups

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UR - https://www.scopus.com/pages/publications/85078161564#tab=citedBy

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SP - 86

EP - 107

JO - Journal of Algebra

JF - Journal of Algebra

ER -

The average character degree and an improvement of the Itô-Michler theorem

Abstract

Keywords

ASJC Scopus subject areas

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