Degrees of Brauer characters in 𝑝-solvable groups

1987 ◽  
pp. 485-487
Author(s):  
Thomas R. Wolf
Keyword(s):  
Solvable Groups ◽  
Brauer Characters

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 The $q$-parts of degrees of Brauer characters of solvable groups

1989 ◽  
Vol 33 (4) ◽  
pp. 583-591 ◽  
Author(s):  
Olaf Manz ◽  
Thomas R. Wolf
Keyword(s):  
Solvable Groups ◽  
Brauer Characters

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].

scholarly journals Lifting Brauer characters ofp-solvable groups

1974 ◽  
Vol 53 (1) ◽  
pp. 171-188 ◽  
Author(s):  
I. Martin Isaacs
Keyword(s):  
Solvable Groups ◽  
Brauer Characters

Character Correspondences and π-Special Characters in π-Separable Groups

1987 ◽  
Vol 39 (4) ◽  
pp. 920-937 ◽  
Author(s):  
Thomas R. Wolf
Keyword(s):  
Irreducible Character ◽  
Solvable Groups ◽  
Character Theory ◽  
Separable Group ◽  
Irreducible Characters ◽  
Special Character ◽  
Brauer Characters ◽  
One To One

Let π be a set of primes and let G be a π-separable group (all groups considered are finite). Two subsets Xπ(G) and Bπ(G) of the set Irr(G) of irreducible characters of G play an important role in the character theory of π-separable groups and particularly solvable groups. If p is prime and π is the set of all other primes, then the Bπ characters of G give a natural one-to-one lift of the Brauer characters of G into Irr(G). More generally, they have been used to define Brauer characters for sets of primes.The π-special characters of G (i.e., Xπ(G)) restrict irreducibly and in a one-to-one fashion to a Hall-π-subgroup of G. If an irreducible character χ is quasi-primitive, it factors uniquely as a product of a π-special character an a π′-special character. This is a particularly useful tool in solvable groups.

scholarly journals Brauer characters of q′-degree in p-solvable groups

1988 ◽  
Vol 115 (1) ◽  
pp. 75-91 ◽  
Author(s):  
Olaf Manz ◽  
Thomas R Wolf
Keyword(s):  
Solvable Groups ◽  
Brauer Characters
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