scholarly journals Groups with One or Two Super-Brauer Character Theories

2020 ◽  
Vol 36 (4) ◽  
pp. 379-394
Author(s):  
Xiao You Chen ◽  
Mark L. Lewis
Keyword(s):  
Brauer Character

A Note on Brauer Character Degrees of Solvable Groups

1991 ◽  
Vol 34 (3) ◽  
pp. 423-425 ◽  
Author(s):  
You-Qiang Wang
Keyword(s):  
Solvable Group ◽  
Solvable Groups ◽  
Character Degrees ◽  
Finite Solvable Group ◽  
Prime Integer ◽  
Derived Length ◽  
Brauer Character ◽  
Brauer Characters

AbstractLet G be a finite solvable group. Fix a prime integer p and let t be the number of distinct degrees of irreducible Brauer characters of G with respect to the prime p. We obtain the bound 3t — 2 for the derived length of a Hall p'-subgroup of G. Furthermore, if |G| is odd, then the derived length of a Hall p'-subgroup of G is bounded by /.

scholarly journals Low-Dimensional Representations of Quasi-Simple Groups

2001 ◽  
Vol 4 ◽  
pp. 22-63 ◽  
Author(s):  
Gerhard Hiss ◽  
Gunter Malle
Keyword(s):  
Finite Groups ◽  
Irreducible Representations ◽  
Simple Groups ◽  
Additional Information ◽  
Brauer Character ◽  
Low Dimensional

AbstractThe authors determine all the absolutely irreducible representations of degree up to 250 of quasi-simple finite groups, excluding groups that are of Lie type in their defining characteristic. Additional information is also given on the Frobenius-Schur indicators and the Brauer character fields of the representations.

scholarly journals Sylow Normalizers and Brauer Character Degrees

2000 ◽  
Vol 229 (2) ◽  
pp. 623-631
Author(s):  
Antonio Beltrán ◽  
Gabriel Navarro
Keyword(s):  
Character Degrees ◽  
Brauer Character

Blocks of small defect in alternating groups and squares of Brauer character degrees

2017 ◽  
Vol 20 (6) ◽  
Author(s):  
Xiaoyou Chen ◽  
James P. Cossey ◽  
Mark L. Lewis ◽  
Hung P. Tong-Viet
Keyword(s):  
Character Degrees ◽  
Alternating Groups ◽  
Brauer Character ◽  
Small Defect

AbstractLet

Some conjectures on Brauer character degrees

2020 ◽  
Vol 550 ◽  
pp. 210-218
Author(s):  
Hung P. Tong-Viet
Keyword(s):  
Character Degrees ◽  
Brauer Character

scholarly journals p -Parts of Brauer character degrees

2014 ◽  
Vol 403 ◽  
pp. 426-438 ◽  
Author(s):  
Gabriel Navarro ◽  
Pham Huu Tiep ◽  
Hung P. Tong-Viet
Keyword(s):  
Character Degrees ◽  
Brauer Character

scholarly journals NONVANISHING ELEMENTS FOR BRAUER CHARACTERS

2015 ◽  
Vol 102 (1) ◽  
pp. 96-107 ◽  
Author(s):  
SILVIO DOLFI ◽  
EMANUELE PACIFICI ◽  
LUCIA SANUS
Keyword(s):  
Finite Group ◽  
Normal Subgroup ◽  
Finite Groups ◽  
Regular Element ◽  
Solvable Groups ◽  
Vector Spaces ◽  
Brauer Character ◽  
Brauer Characters ◽  
A Finite Group ◽  
Finite Vector Spaces

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 $g\in G$ is a $p$-regular element which is $p$-nonvanishing, then $g$ lies in a normal subgroup of $G$ whose $p$-length and $p^{\prime }$-length are both at most 2 (with possible exceptions for $p\leq 7$), 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].

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