Character degree graphs with no complete vertices

被引：7

作者：

Zuccari, Claudio Paolo Morresi ^{[1
]}

机构：

[1] Univ Aquila, Dipartimento Matemat Pura & Applicata, I-67010 Coppito, Laquila, Italy

来源：

JOURNAL OF ALGEBRA | 2012年 / 353卷 / 01期

关键词：

Finite solvable groups; Representations and characters; Graphs; SOLVABLE-GROUPS;

D O I：

10.1016/j.jalgebra.2011.11.029

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let Gamma be a graph in which each vertex is non-adjacent to another different one. We show that, if G is a finite solvable group with abelian Fitting subgroup and with character degree graph Gamma(G) = Gamma, then G is a direct product of subgroups having a disconnected character degree graph. In particular, Gamma is a join of disconnected graphs. We deduce also that solvable groups with abelian Fitting subgroup have a character degree graph with diameter at most 2. (C) 2011 Elsevier Inc. All rights reserved.

引用

页码：22 / 30

页数：9

共 8 条

[1] Isaacs I. M., 2006, CHARACTER THEORY FIN
[2] A solvable group whose character degree graph has diameter 3
Lewis, ML
[J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2002, 130 (03) : 625 - 630
[3] Bounding fitting heights of character degree graphs
Lewis, ML
[J]. JOURNAL OF ALGEBRA, 2001, 242 (02) : 810 - 818
[4] Solvable groups whose degree graphs have two connected components
Lewis, ML
[J]. JOURNAL OF GROUP THEORY, 2001, 4 (03) : 255 - 275
[5] Manz O., 1993, Representations of Solvable Groups
[6] Palfy P. P., 1998, PERIOD MATH HUNG, V36, P61
[7] On the character degree graph of solvable groups.: II.: Disconnected graphs
Pálfy, PP
[J]. STUDIA SCIENTIARUM MATHEMATICARUM HUNGARICA, 2001, 38 : 339 - 355
[8] Finite solvable groups whose character degree graphs are not complete
Zhang, Jiping
[J]. ALGEBRA COLLOQUIUM, 2006, 13 (04) : 541 - 552

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