On Some Graphs of Finite Metabelian Groups of Order Less Than 24

IF 0.3 Q4 MATHEMATICS Matematika Pub Date : 2019-07-31 DOI:10.11113/MATEMATIKA.V35.N2.1054
I. Gambo, N. Sarmin, S. Omer
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引用次数: 0

Abstract

In this work, a non-abelian metabelian group is represented by G while represents conjugacy class graph. Conjugacy class graph of a group is that graph associated with the conjugacy classes of the group. Its vertices are the non-central conjugacy classes of the group, and two distinct vertices are joined by an edge if their cardinalities are not coprime. A group is referred to as metabelian if there exits an abelian normal subgroup in which the factor group is also abelian. It has been proven earlier that 25 non-abelian metabelian groups which have order less than 24, which are considered in this work, exist. In this article, the conjugacy class graphs of non-abelian metabelian groups of order less than 24 are determined as well as examples of some finite groups associated to other graphs are given.
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关于小于24阶有限亚生意人群的若干图
在这项工作中,一个非阿贝尔偏旁群用G表示,而表示共轭类图。群的共轭类图是与群的共轭类相关联的图。它的顶点是群的非中心共轭类,如果两个不同的顶点的基数不互质,则它们通过边连接。如果存在一个阿贝尔正规子群,其中因子群也是阿贝尔的,则一个群被称为代谢亚群。先前已经证明,本工作中考虑的25个阶数小于24的非阿贝尔代谢亚群存在。本文确定了小于24阶的非阿贝尔偏贝列群的共轭类图,并给出了一些与其它图相关的有限群的例子。
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来源期刊
Matematika
Matematika MATHEMATICS-
自引率
25.00%
发文量
0
审稿时长
24 weeks
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