scholarly journals Character degrees of extensions of the Suzuki groups 2B2(q2)

2018 ◽  
Vol 17 (01) ◽  
pp. 1850006 ◽  
Author(s):  
Mehdi Ghaffarzadeh
Keyword(s):  
Character Degrees ◽  
Irreducible Characters ◽  
Suzuki Group ◽  
Suzuki Groups

Let [Formula: see text] be a Suzuki group [Formula: see text], where [Formula: see text], [Formula: see text]. In this paper, we determine the degrees of the ordinary complex irreducible characters of every group [Formula: see text] such that [Formula: see text].

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.

Coprime Group Actions Fixing All Nonlinear Irreducible Characters

1989 ◽  
Vol 41 (1) ◽  
pp. 68-82 ◽  
Author(s):  
I. M. Isaacs
Keyword(s):  
Finite Groups ◽  
Irreducible Character ◽  
Group Actions ◽  
Character Degrees ◽  
Prime Divisors ◽  
Irreducible Characters ◽  
Nilpotent Length ◽  
Derived Subgroup ◽  
Nonlinear Irreducible Character

The main result of this paper is the following:Theorem A. Let H and N be finite groups with coprime orders andsuppose that H acts nontrivially on N via automorphisms. Assume that Hfixes every nonlinear irreducible character of N. Then the derived subgroup ofN is nilpotent and so N is solvable of nilpotent length≦ 2.Why might one be interested in a situation like this? There has been considerable interest in the question of what one can deduce about a group Gfrom a knowledge of the setcd(G) = ﹛x(l)lx ∈ Irr(G) ﹜of irreducible character degrees of G.Recently, attention has been focused on the prime divisors of the elements of cd(G). For instance, in [9], O. Manz and R. Staszewski consider π-separable groups (for some set π of primes) with the property that every element of cd(G) is either a 77-number or a π'-number.

scholarly journals Irreducible characters of even degree and normal Sylow 2-subgroups

2016 ◽  
Vol 162 (2) ◽  
pp. 353-365 ◽  
Author(s):  
NGUYEN NGOC HUNG ◽  
PHAM HUU TIEP
Keyword(s):  
Finite Group ◽  
Finite Groups ◽  
Irreducible Character ◽  
Average Degree ◽  
Character Degrees ◽  
Irreducible Characters ◽  
A Finite Group

AbstractThe classical Itô-Michler theorem on character degrees of finite groups asserts that if the degree of every complex irreducible character of a finite group G is coprime to a given prime p, then G has a normal Sylow p-subgroup. We propose a new direction to generalize this theorem by introducing an invariant concerning character degrees. We show that if the average degree of linear and even-degree irreducible characters of G is less than 4/3 then G has a normal Sylow 2-subgroup, as well as corresponding analogues for real-valued characters and strongly real characters. These results improve on several earlier results concerning the Itô-Michler theorem.

scholarly journals On Groups Whose Irreducible Character Degrees of All Proper Subgroups are All Prime Powers

2021 ◽  
Vol 2021 ◽  
pp. 1-7
Author(s):  
Shitian Liu
Keyword(s):  
Finite Groups ◽  
Irreducible Character ◽  
Prime Power ◽  
Character Degree ◽  
Character Degrees ◽  
Simple Groups ◽  
Nonsolvable Group ◽  
Irreducible Characters ◽  
Almost Simple Groups

Isaacs, Passman, and Manz have determined the structure of finite groups whose each degree of the irreducible characters is a prime power. In particular, if G is a nonsolvable group and every character degree of a group G is a prime power, then G is isomorphic to S × A , where S ∈ A 5 , PSL 2 8 and A is abelian. In this paper, we change the condition, each character degree of a group G is a prime power, into the condition, each character degree of the proper subgroups of a group is a prime power, and give the structure of almost simple groups whose character degrees of all proper subgroups are all prime powers.

Character Degree Graphs of Solvable Groups of Fitting Height 2

2006 ◽  
Vol 49 (1) ◽  
pp. 127-133 ◽  
Author(s):  
Mark L. Lewis
Keyword(s):  
Finite Group ◽  
Solvable Group ◽  
Irreducible Character ◽  
Solvable Groups ◽  
Character Degree ◽  
Character Degrees ◽  
Irreducible Characters ◽  
Vertex Set ◽  
Fitting Height ◽  
A Finite Group

AbstractGiven a finite group G, we attach to the character degrees of G a graph whose vertex set is the set of primes dividing the degrees of irreducible characters of G, and with an edge between p and q if pq divides the degree of some irreducible character of G. In this paper, we describe which graphs occur when G is a solvable group of Fitting height 2.

COPRIME COMMUTATORS IN THE SUZUKI GROUPS

2021 ◽  
pp. 1-5
Author(s):  
GIOVANNI ZINI
Keyword(s):  
Suzuki Group ◽  
Suzuki Groups

Abstract In this note we show that every element of a simple Suzuki group $^2B_2(q)$ is a commutator of elements of coprime orders.

A NOTE ON DERIVED LENGTH AND CHARACTER DEGREES

2020 ◽  
pp. 1-7
Author(s):  
BURCU ÇINARCI ◽  
TEMHA ERKOÇ
Keyword(s):  
Solvable Group ◽  
Irreducible Character ◽  
Commutator Subgroup ◽  
Sufficient Conditions ◽  
Character Degrees ◽  
Finite Solvable Group ◽  
Irreducible Characters ◽  
Derived Length

Isaacs and Seitz conjectured that the derived length of a finite solvable group $G$ is bounded by the cardinality of the set of all irreducible character degrees of $G$ . We prove that the conjecture holds for $G$ if the degrees of nonlinear monolithic characters of $G$ having the same kernels are distinct. Also, we show that the conjecture is true when $G$ has at most three nonlinear monolithic characters. We give some sufficient conditions for the inequality related to monolithic characters or real-valued irreducible characters of $G$ when the commutator subgroup of $G$ is supersolvable.

Schur indices and irreducible character degrees in finite solvable groups

1989 ◽  
Vol 105 (2) ◽  
pp. 237-240 ◽  
Author(s):  
R. Gow
Keyword(s):  
Finite Group ◽  
Irreducible Character ◽  
Group Structure ◽  
Solvable Groups ◽  
Character Degrees ◽  
Irreducible Characters ◽  
A Finite Group

Let G be a finite group and let Irr(G) denote the set of complex irreducible characters of G. Various authors have investigated the question of how information about the degrees of the characters in Irr (G) can provide information about the structure of G. Chapter 12 of [2] gives a survey of a number of results arising from such questions. Two well-known examples of theorems that relate character degrees and group structure are those due to Thompson (12·2 in [2]) and Itô (12.34 in [2]), which we recall here.

scholarly journals Character degrees in 𝜋-separable groups

2020 ◽  
Vol 23 (6) ◽  
pp. 1069-1080
Author(s):  
Nicola Grittini
Keyword(s):  
Character Degrees ◽  
Character Theory ◽  
Irreducible Characters

AbstractIf a group G is π-separable, where π is a set of primes, the set of irreducible characters {\operatorname{B}_{\pi}(G)\cup\operatorname{B}_{\pi^{\prime}}(G)} can be defined. In this paper, we prove variants of some classical theorems in character theory, namely the theorem of Ito–Michler and Thompson’s theorem on character degrees, involving irreducible characters in the set {\operatorname{B}_{\pi}(G)\cup\operatorname{B}_{\pi^{\prime}}(G)}.

ANALYSIS OF THE IMPLEMENTATION COMPLEXITY OF CRYPTOSYSTEM BASED ON THE SUZUKI GROUP

2019 ◽  
Vol 78 (5) ◽  
pp. 419-427 ◽  
Author(s):  
G. Z. Khalimov ◽  
E. V. Kotukh ◽  
Yu. O. Serhiychuk ◽  
O. S. Marukhnenko
Keyword(s):  
Suzuki Group
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