Character degrees in separable groups

2021 ◽  
Author(s):  
Gabriel Navarro ◽  
Noelia Rizo ◽  
Lucía Sanus
Keyword(s):  
Character Degrees

scholarly journals A new characterization of L2(p2)

2020 ◽  
Vol 18 (1) ◽  
pp. 907-915
Author(s):  
Zhongbi Wang ◽  
Chao Qin ◽  
Heng Lv ◽  
Yanxiong Yan ◽  
Guiyun Chen
Keyword(s):  
Positive Integer ◽  
Irreducible Character ◽  
Character Degrees ◽  
Prime Divisors

Abstract For a positive integer n and a prime p, let {n}_{p} denote the p-part of n. Let G be a group, \text{cd}(G) the set of all irreducible character degrees of G , \rho (G) the set of all prime divisors of integers in \text{cd}(G) , V(G)=\left\{{p}^{{e}_{p}(G)}|p\in \rho (G)\right\} , where {p}^{{e}_{p}(G)}=\hspace{.25em}\max \hspace{.25em}\{\chi {(1)}_{p}|\chi \in \text{Irr}(G)\}. In this article, it is proved that G\cong {L}_{2}({p}^{2}) if and only if |G|=|{L}_{2}({p}^{2})| and V(G)=V({L}_{2}({p}^{2})) .

Complex group algebras of the direct product of non-isomorphic Suzuki groups

2019 ◽  
Vol 19 (02) ◽  
pp. 2050036
Author(s):  
Morteza Baniasad Azad ◽  
Behrooz Khosravi
Keyword(s):  
Direct Product ◽  
Group Algebra ◽  
Irreducible Character ◽  
Prime Numbers ◽  
Product Formula ◽  
Character Degrees ◽  
Group Algebras ◽  
Complex Group ◽  
Complex Group Algebra ◽  
Suzuki Groups

In this paper, we prove that the direct product [Formula: see text], where [Formula: see text] are distinct numbers, is uniquely determined by its complex group algebra. Particularly, we show that the direct product [Formula: see text], where [Formula: see text]’s are distinct odd prime numbers, is uniquely determined by its order and three irreducible character degrees.

scholarly journals 𝑝-groups with exactly four codegrees

2020 ◽  
Vol 23 (6) ◽  
pp. 1111-1122
Author(s):  
Sarah Croome ◽  
Mark L. Lewis
Keyword(s):  
Irreducible Character ◽  
Character Degree ◽  
Character Degrees ◽  
Additional Hypothesis ◽  
Nilpotence Class ◽  
Irreducible Character Degree

AbstractLet G be a p-group, and let χ be an irreducible character of G. The codegree of χ is given by {\lvert G:\operatorname{ker}(\chi)\rvert/\chi(1)}. Du and Lewis have shown that a p-group with exactly three codegrees has nilpotence class at most 2. Here we investigate p-groups with exactly four codegrees. If, in addition to having exactly four codegrees, G has two irreducible character degrees, G has largest irreducible character degree {p^{2}}, {\lvert G:G^{\prime}\rvert=p^{2}}, or G has coclass at most 3, then G has nilpotence class at most 4. In the case of coclass at most 3, the order of G is bounded by {p^{7}}. With an additional hypothesis, we can extend this result to p-groups with four codegrees and coclass at most 6. In this case, the order of G is bounded by {p^{10}}.

scholarly journals Taketa's theorem for relative character degrees

2013 ◽  
Vol 43 (5) ◽  
pp. 1451-1457
Author(s):  
Kamal Aziziheris
Keyword(s):  
Character Degrees

scholarly journals Actions and Invariant Character Degrees

1993 ◽  
Vol 160 (1) ◽  
pp. 172-178 ◽  
Author(s):  
G. Navarro
Keyword(s):  
Character Degrees

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].

scholarly journals Actions and Invariant Character Degrees, II

1996 ◽  
Vol 184 (2) ◽  
pp. 397-406 ◽  
Author(s):  
Gabriel Navarro
Keyword(s):  
Character Degrees

scholarly journals Character degrees in blocks and defect groups

2021 ◽  
Author(s):  
Eugenio Giannelli ◽  
J. Miquel Martínez ◽  
A.A. Schaeffer Fry
Keyword(s):  
Character Degrees ◽  
Defect Groups

scholarly journals Hook lengths in a skew Young diagram

10.37236/1309 ◽  
1997 ◽  
Vol 4 (1) ◽  
Author(s):  
Svante Janson
Keyword(s):  
Young Diagram ◽  
Character Degrees ◽  
Young Diagrams ◽  
Inductive Proof

Regev and Vershik (Electronic J. Combinatorics 4 (1997), #R22) have obtained some properties of the set of hook lengths for certain skew Young diagrams, using asymptotic calculations of character degrees. They also conjectured a stronger form of one of their results. We give a simple inductive proof of this conjecture. Very recently, Regev and Zeilberger (Annals of Combinatorics, to appear) have independently proved this conjecture.

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