Solvable groups whose character degree graphs generalize squares

被引：1

作者：

Lewis, Mark L. ^{[1
]}

Meng, Qingyun ^{[2
]}

机构：

[1] Kent State Univ, Dept Math Sci, Kent, OH 44242 USA

[2] Henan Univ Technol, Coll Sci, Zhengzhou 450001, Peoples R China

来源：

JOURNAL OF GROUP THEORY | 2020年 / 23卷 / 02期

基金：

美国国家科学基金会;

关键词：

DIAMETER;

D O I：

10.1515/jgth-2019-0027

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let 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.

引用

页码：217 / 234

页数：18

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