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

Authors

  • Ibrahim Gambo Department of Mathematical Sciences, Universiti Teknologi Malaysia, 81310 UTM Johor Bahru, Malaysia Department of Mathematics, Faculty of Science, Bauchi State University Gadau, Nigeria
  • Nor Haniza Sarmin Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia
  • Sanaa Mohamed Saleh Omer Department of Mathematics, Faculty of Science, University of Benghazi, Benghazi, Libya

DOI:

https://doi.org/10.11113/matematika.v35.n2.1054

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.

Author Biography

Nor Haniza Sarmin, Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia

A Professor of Mathematics at Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia

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Published

2019-07-31

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Articles