Groups whose character degree graph has diameter three

被引：11

作者：

Casolo, Carlo ^{[1
]}

Dolfi, Silvio ^{[1
]}

Pacifici, Emanuele ^{[2
]}

Sanus, Lucia ^{[3
]}

机构：

[1] Univ Florence, Dipartimento Matemat & Informat U Dini, Viale Morgagni 67-A, I-50134 Florence, Italy

[2] Univ Milan, Dipartimento Matemat F Enriques, Via Saldini 50, I-20133 Milan, Italy

[3] Univ Valencia, Fac Matemat, Dept Matemat, E-46100 Valencia, Spain

来源：

ISRAEL JOURNAL OF MATHEMATICS | 2016年 / 215卷 / 02期

关键词：

SOLVABLE-GROUPS;

D O I：

10.1007/s11856-016-1387-5

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let G be a finite group, and let Delta(G) denote the prime graph built on the set of degrees of the irreducible complex characters of G. It is well known that, whenever Delta(G) is connected, the diameter of Delta(G) is at most 3. In the present paper, we provide a description of the finite solvable groups for which the diameter of this graph attains the upper bound. This also enables us to confirm a couple of conjectures proposed by M. L. Lewis.

引用

页码：523 / 558

页数：36

共 50 条

[21] CHARACTER DEGREE GRAPH OF SOLVABLE GROUPS WITH ODD DEGREE
Sivanesan, G.
Selvaraj, C.
arXiv, 2023,
[22] Rational Groups whose character degree graphs are disconnected
Erkoc, Temha
Akar, Gamze
COMPTES RENDUS MATHEMATIQUE, 2022, 360 (01) : 711 - 715
[23] Finite solvable groups whose character degree graphs are not complete
Zhang, Jiping
ALGEBRA COLLOQUIUM, 2006, 13 (04) : 541 - 552
[24] Finite Groups Whose Character Degree Graphs Are Empty Graphs
Meng, Qingyun
Zeng, Jiwen
ALGEBRA COLLOQUIUM, 2013, 20 (01) : 75 - 80
[25] Solvable groups whose character degree graphs generalize squares
Lewis, Mark L.
Meng, Qingyun
JOURNAL OF GROUP THEORY, 2020, 23 (02) : 217 - 234
[26] The Taketa Problem and Character Degree Graphs with Diameter Three
Mark L. Lewis
Catherine B. Sass
Algebras and Representation Theory, 2015, 18 : 1395 - 1399
[27] The Taketa Problem and Character Degree Graphs with Diameter Three
Lewis, Mark L.
Sass, Catherine B.
ALGEBRAS AND REPRESENTATION THEORY, 2015, 18 (05) : 1395 - 1399
[28] The Chromatic Index of a Graph Whose Core has Maximum Degree 2
Akbari, S.
Ghanbari, M.
Kano, M.
Nikmehr, M. J.
ELECTRONIC JOURNAL OF COMBINATORICS, 2012, 19 (01):
[29] THE CHROMATIC INDEX OF A GRAPH WHOSE CORE HAS MAXIMUM DEGREE 2
HILTON, AJW
CHENG, Z
DISCRETE MATHEMATICS, 1992, 101 (1-3) : 135 - 147
[30] Finite groups whose character degree graphs coincide with their prime graphs
Erkoc, Temha
Yilmazturk, Utku
Guloglu, Ismail S.
CZECHOSLOVAK MATHEMATICAL JOURNAL, 2018, 68 (03) : 647 - 656

← 1 2 3 4 5 →