scholarly journals Bounds on the number of lifts of a Brauer character in a p-solvable group

2007 ◽  
Vol 312 (2) ◽  
pp. 699-708 ◽  
Author(s):  
James P. Cossey
Keyword(s):  
Solvable Group ◽  
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 ITÔ’S THEOREM AND MONOMIAL BRAUER CHARACTERS

2017 ◽  
Vol 96 (3) ◽  
pp. 426-428 ◽  
Author(s):  
XIAOYOU CHEN ◽  
MARK L. LEWIS
Keyword(s):  
Solvable Group ◽  
Finite Solvable Group ◽  
Brauer Character ◽  
Brauer Characters

Let $G$ be a finite solvable group and let $p$ be a prime. In this note, we prove that $p$ does not divide $\unicode[STIX]{x1D711}(1)$ for every irreducible monomial $p$-Brauer character $\unicode[STIX]{x1D711}$ of $G$ if and only if $G$ has a normal Sylow $p$-subgroup.

𝒫-characters and the structure of finite solvable groups

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Jiakuan Lu ◽  
Kaisun Wu ◽  
Wei Meng
Keyword(s):  
Finite Group ◽  
Maximal Subgroup ◽  
Solvable Group ◽  
Irreducible Character ◽  
Solvable Groups ◽  
Irreducible Constituent ◽  
A Finite Group

AbstractLet 𝐺 be a finite group. An irreducible character of 𝐺 is called a 𝒫-character if it is an irreducible constituent of (1_{H})^{G} for some maximal subgroup 𝐻 of 𝐺. In this paper, we obtain some conditions for a solvable group 𝐺 to be 𝑝-nilpotent or 𝑝-closed in terms of 𝒫-characters.

Bounding Fitting Heights of Two Classes of Character Degree Graphs

2014 ◽  
Vol 21 (02) ◽  
pp. 355-360
Author(s):  
Xianxiu Zhang ◽  
Guangxiang Zhang
Keyword(s):  
Solvable Group ◽  
Disjoint Union ◽  
Character Degree ◽  
Finite Solvable Group ◽  
Total Degree ◽  
Character Degree Graph ◽  
Vertex Set ◽  
Fitting Height ◽  
Degree Graph

In this article, we prove that a finite solvable group with character degree graph containing at least four vertices has Fitting height at most 4 if each derived subgraph of four vertices has total degree not more than 8. We also prove that if the vertex set ρ(G) of the character degree graph Δ(G) of a solvable group G is a disjoint union ρ(G) = π1 ∪ π2, where |πi| ≥ 2 and pi, qi∈ πi for i = 1,2, and no vertex in π1 is adjacent in Δ(G) to any vertex in π2 except for p1p2 and q1q2, then the Fitting height of G is at most 4.

Group Algebras with Minimal Strong Lie Derived Length

2008 ◽  
Vol 51 (2) ◽  
pp. 291-297 ◽  
Author(s):  
Ernesto Spinelli
Keyword(s):  
Solvable Group ◽  
Group Algebra ◽  
Positive Characteristic ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Group Algebras ◽  
Derived Length ◽  
Necessary And Sufficient

AbstractLet KG be a non-commutative strongly Lie solvable group algebra of a group G over a field K of positive characteristic p. In this note we state necessary and sufficient conditions so that the strong Lie derived length of KG assumes its minimal value, namely [log2(p + 1)].

ITÔ’S THEOREM AND MONOMIAL BRAUER CHARACTERS II

2017 ◽  
Vol 97 (2) ◽  
pp. 215-217
Author(s):  
XIAOYOU CHEN ◽  
MARK L. LEWIS
Keyword(s):  
Solvable Group ◽  
Finite Solvable Group ◽  
Brauer Characters

Let $G$ be a finite solvable group and let $p$ be a prime. We prove that the intersection of the kernels of irreducible monomial $p$-Brauer characters of $G$ with degrees divisible by $p$ is $p$-closed.

Real characters, monolithic characters and the Taketa inequality

2019 ◽  
Vol 18 (10) ◽  
pp. 1950183 ◽  
Author(s):  
Burcu Çınarcı ◽  
Temha Erkoç
Keyword(s):  
Solvable Group ◽  
Character Degrees ◽  
Finite Solvable Group ◽  
Complex Character ◽  
The Real ◽  
Derived Length

In this paper, we prove that the Taketa inequality, namely the derived length of a finite solvable group [Formula: see text] is less than or equal to the number of distinct irreducible complex character degrees of [Formula: see text], is true under some conditions related to the real and the monolithic characters of [Formula: see text].

The 2-length and 2-period of a finite solvable group

1979 ◽  
Vol 18 (1) ◽  
pp. 5-20 ◽  
Author(s):  
E. G. Bryukhanova
Keyword(s):  
Solvable Group ◽  
Finite Solvable Group

Derived length when a product of characters has two nonprincipal irreducible constituents

2016 ◽  
Vol 15 (06) ◽  
pp. 1650110
Author(s):  
Lisa Rose Hendrixson ◽  
Mark L. Lewis
Keyword(s):  
Solvable Group ◽  
Irreducible Character ◽  
Character Formula ◽  
Derived Length

We study the situation where a solvable group [Formula: see text] has a faithful irreducible character [Formula: see text] such that [Formula: see text] has exactly two distinct nonprincipal irreducible constituents. We prove that [Formula: see text] has derived length bounded above by 8, and provide an example of such a group having derived length 8. In particular, this improves upon a result of Adan-Bante.

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