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

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 Solvable groups whose character degree graphs generalize squares

2020 ◽  
Vol 23 (2) ◽  
pp. 217-234
Author(s):  
Mark L. Lewis ◽  
Qingyun Meng
Keyword(s):  
Solvable Group ◽  
Solvable Groups ◽  
Character Degree ◽  
Sylow Subgroups ◽  
Character Degree Graph ◽  
Product Of Subgroups ◽  
Degree Graph ◽  
Delta G ◽  
Definition Of ◽  
Square Graph

AbstractLet G be a solvable group, and let {\Delta(G)} be the character degree graph of G. In this paper, we generalize the definition of a square graph to graphs that are block squares. We show that if G is a solvable group so that {\Delta(G)} is a block square, then G has at most two normal nonabelian Sylow subgroups. Furthermore, we show that when G is a solvable group that has two normal nonabelian Sylow subgroups and {\Delta(G)} is block square, then G is a direct product of subgroups having disconnected character degree graphs.

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.

scholarly journals Thep-Length of a Solvable Group Bounded by Conditions on its Character Degree Graph

1996 ◽  
Vol 186 (1) ◽  
pp. 162-181 ◽  
Author(s):  
Judith Pense
Keyword(s):  
Solvable Group ◽  
Character Degree ◽  
Character Degree Graph ◽  
Degree Graph

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

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

Fitting heights and the character degree graph

2000 ◽  
Vol 75 (5) ◽  
pp. 338-341 ◽  
Author(s):  
M.L. Lewis
Keyword(s):  
Character Degree ◽  
Character Degree Graph ◽  
Degree Graph

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

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
Sign in / Sign up

Export Citation Format

Share Document