On some graphs of finite metabelian groups of order less than 24

• Main Authors: Gambo, Ibrahim, Sarmin, Nor Haniza, Mohamed Saleh Omer, Sanaa
• Format: Article
• Language: English
• Published: Penerbit UTM Press 2019
• Subjects: QA Mathematics
• Online Access: http://eprints.utm.my/id/eprint/89017/1/NorHanizaSarmin2019_OnSomeGraphsofFiniteMetabelianGroups.pdf; http://eprints.utm.my/id/eprint/89017/; http://dx.doi.org/10.11113/matematika.v35.n2.1054

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.