Let G be a finite group and p a prime. We say that a p-regular element g of G is p-nonvanishing if no irreducible p-Brauer character of G takes the value 0 on g. The main result of this paper shows that if G is solvable and g ∈ G is a p-regular element which is p-nonvanishing, then g lies in a normal subgroup of G whose p-length and p -length are both at most 2 (with possible exceptions for p ≤ 7), the bound being best possible. This result is obtained through the analysis of one particular orbit condition in linear actions of solvable groups on finite vector spaces, and it generalizes (for p > 7) some results in Dolfi and Pacifici [‘Zeros of Brauer characters and linear actions of finite groups’, J. Algebra 340 (2011), 104–113].

NONVANISHING ELEMENTS FOR BRAUER CHARACTERS / Dolfi, Silvio; Pacifici, Emanuele; Sanus, Lucia. - In: JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY. - ISSN 1446-7887. - STAMPA. - 102:(2017), pp. 96-107. [10.1017/S1446788715000178]

NONVANISHING ELEMENTS FOR BRAUER CHARACTERS

DOLFI, SILVIO;PACIFICI, EMANUELE;
2017

Abstract

Let G be a finite group and p a prime. We say that a p-regular element g of G is p-nonvanishing if no irreducible p-Brauer character of G takes the value 0 on g. The main result of this paper shows that if G is solvable and g ∈ G is a p-regular element which is p-nonvanishing, then g lies in a normal subgroup of G whose p-length and p -length are both at most 2 (with possible exceptions for p ≤ 7), the bound being best possible. This result is obtained through the analysis of one particular orbit condition in linear actions of solvable groups on finite vector spaces, and it generalizes (for p > 7) some results in Dolfi and Pacifici [‘Zeros of Brauer characters and linear actions of finite groups’, J. Algebra 340 (2011), 104–113].
2017
102
96
107
Dolfi, Silvio; Pacifici, Emanuele; Sanus, Lucia
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Utilizza questo identificatore per citare o creare un link a questa risorsa: https://hdl.handle.net/2158/1071669
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