scholarly journals Recognition of characteristically simple group $A_5\times A_5$ by character degree graph and order

2018 ◽  
Vol 68 (4) ◽  
pp. 1149-1157
Author(s):  
Maryam Khademi ◽  
Behrooz Khosravi
Keyword(s):  
Simple Group ◽  
Character Degree ◽  
Character Degree Graph ◽  
Degree Graph

Recognition of the simple group PSL( $$2,p^{2}$$ 2 , p 2 ) by character degree graph and order

2014 ◽  
Vol 178 (2) ◽  
pp. 251-257 ◽  
Author(s):  
Behrooz Khosravi ◽  
Behnam Khosravi ◽  
Bahman Khosravi ◽  
Zahra Momen
Keyword(s):  
Simple Group ◽  
Character Degree ◽  
Character Degree Graph ◽  
Degree Graph

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.

BOUNDING THE NUMBER OF IRREDUCIBLE CHARACTER DEGREES OF A FINITE GROUP IN TERMS OF THE LARGEST DEGREE

2013 ◽  
Vol 13 (02) ◽  
pp. 1350096 ◽  
Author(s):  
MARK L. LEWIS ◽  
ALEXANDER MORETÓ
Keyword(s):  
Finite Group ◽  
Irreducible Character ◽  
Character Degree ◽  
Character Degrees ◽  
Character Degree Graph ◽  
Prime Factors ◽  
Degree Graph ◽  
A Finite Group

We conjecture that the number of irreducible character degrees of a finite group is bounded in terms of the number of prime factors (counting multiplicities) of the largest character degree. We prove that this conjecture holds when the largest character degree is prime and when the character degree graph is disconnected.

scholarly journals On the character degree graph of finite groups

2019 ◽  
Vol 198 (5) ◽  
pp. 1595-1614 ◽  
Author(s):  
Zeinab Akhlaghi ◽  
Carlo Casolo ◽  
Silvio Dolfi ◽  
Emanuele Pacifici ◽  
Lucia Sanus
Keyword(s):  
Finite Groups ◽  
Character Degree ◽  
Character Degree Graph ◽  
Degree Graph

On the character degree graph of solvable groups. II. Discon- nected graphs

2001 ◽  
Vol 38 (1-4) ◽  
pp. 339-355 ◽  
Author(s):  
P. P. Pálfy
Keyword(s):  
Solvable Group ◽  
Irreducible Character ◽  
Solvable Groups ◽  
Character Degree ◽  
Finite Solvable Group ◽  
Nilpotent Length ◽  
Character Degree Graph ◽  
Degree Graph

Let G be a finite solvable group and ¡ a set of primes such that the degree of each irreducible character of G is either a ¡-number or a ¡0-number. We show that such groups have a very restricted structure, for example, their nilpotent length is at most 4. We also prove that Huppert's ^{ÿ Conjecture is valid for these groups.

scholarly journals Recognition by character degree graph and order of simple groups of order less than 6000

2014 ◽  
Vol 15 (2) ◽  
pp. 537 ◽  
Author(s):  
Behrooz Khosravi ◽  
Bahman Khosravi ◽  
Behnam Khosravi ◽  
Zahra Momen
Keyword(s):  
Character Degree ◽  
Simple Groups ◽  
Character Degree Graph ◽  
Degree Graph

ON THE REGULARITY OF CHARACTER DEGREE GRAPHS

2019 ◽  
Vol 100 (3) ◽  
pp. 428-433 ◽  
Author(s):  
Z. SAYANJALI ◽  
Z. AKHLAGHI ◽  
B. KHOSRAVI
Keyword(s):  
Finite Group ◽  
Character Degree ◽  
Character Degrees ◽  
Prime Divisors ◽  
Character Degree Graph ◽  
Vertex Set ◽  
Degree Graph ◽  
A Finite Group ◽  
Regular Bipartite Graph ◽  
Complex Characters

Let $G$ be a finite group and let $\text{Irr}(G)$ be the set of all irreducible complex characters of $G$. Let $\unicode[STIX]{x1D70C}(G)$ be the set of all prime divisors of character degrees of $G$. The character degree graph $\unicode[STIX]{x1D6E5}(G)$ associated to $G$ is a graph whose vertex set is $\unicode[STIX]{x1D70C}(G)$, and there is an edge between two distinct primes $p$ and $q$ if and only if $pq$ divides $\unicode[STIX]{x1D712}(1)$ for some $\unicode[STIX]{x1D712}\in \text{Irr}(G)$. We prove that $\unicode[STIX]{x1D6E5}(G)$ is $k$-regular for some natural number $k$ if and only if $\overline{\unicode[STIX]{x1D6E5}}(G)$ is a regular bipartite graph.

scholarly journals On the character degree graph of solvable groups

2017 ◽  
Vol 146 (4) ◽  
pp. 1505-1513 ◽  
Author(s):  
Zeinab Akhlaghi ◽  
Carlo Casolo ◽  
Silvio Dolfi ◽  
Khatoon Khedri ◽  
Emanuele Pacifici
Keyword(s):  
Solvable Groups ◽  
Character Degree ◽  
Character Degree Graph ◽  
Degree Graph
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