Groups with just one character degree divisible by a given prime

I. M. Isaacs; Alexander Moretó; Gabriel Navarro; Pham Huu Tiep

doi:10.1090/S0002-9947-09-04718-7

Groups with just one character degree divisible by a given prime

I. M. Isaacs
, Alexander Moretó
, Gabriel Navarro
, Pham Huu Tiep

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

14 Scopus citations

Abstract

The Ito-Michler theorem asserts that if no irreducible character of a finite group G has degree divisible by some given prime p, then a Sylow p-subgroup of G is both normal and abelian. In this paper we relax the hypothesis, and we assume that there is at exactly one multiple of p that occurs as the degree of an irreducible character of G. We show that in this situation, a Sylow p-subgroup of G is almost normal in G, and it is almost abelian.

Original language	English (US)
Pages (from-to)	6521-6547
Number of pages	27
Journal	Transactions of the American Mathematical Society
Volume	361
Issue number	12
DOIs	https://doi.org/10.1090/S0002-9947-09-04718-7
State	Published - Dec 2009
Externally published	Yes

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

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abstract = "The Ito-Michler theorem asserts that if no irreducible character of a finite group G has degree divisible by some given prime p, then a Sylow p-subgroup of G is both normal and abelian. In this paper we relax the hypothesis, and we assume that there is at exactly one multiple of p that occurs as the degree of an irreducible character of G. We show that in this situation, a Sylow p-subgroup of G is almost normal in G, and it is almost abelian.",

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AU - Moretó, Alexander

AU - Navarro, Gabriel

AU - Tiep, Pham Huu

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Y1 - 2009/12

N2 - The Ito-Michler theorem asserts that if no irreducible character of a finite group G has degree divisible by some given prime p, then a Sylow p-subgroup of G is both normal and abelian. In this paper we relax the hypothesis, and we assume that there is at exactly one multiple of p that occurs as the degree of an irreducible character of G. We show that in this situation, a Sylow p-subgroup of G is almost normal in G, and it is almost abelian.

AB - The Ito-Michler theorem asserts that if no irreducible character of a finite group G has degree divisible by some given prime p, then a Sylow p-subgroup of G is both normal and abelian. In this paper we relax the hypothesis, and we assume that there is at exactly one multiple of p that occurs as the degree of an irreducible character of G. We show that in this situation, a Sylow p-subgroup of G is almost normal in G, and it is almost abelian.

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Groups with just one character degree divisible by a given prime

Abstract

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