The Quartic Commutativity Degree of Dihedral Groups


  • Muhanizah Abdul Hamid School of Mathematical Sciences, College of Computing, Informatics and Mathematics, Universiti Teknologi MARA, 40450 Shah Alam, Selangor, Malaysia
  • Adnin Afifi Nawi Department of Science and Mathematics, Centre for Diploma Science, Universiti Tun Hussein Onn, Pagoh Higher Education Hub, 84600, Pagoh, Johor, Malaysia



Dihedral group, Quartic commutativity degree


The combination of group theory and probability theory was used in studying the connection between the two. In recent years, probability theory has been widely used in solving several difficult problems in group theory. The commutativity degree of a group,  is defined as the probability that two random elements in a group commute. In addition, there exist a generalization of commutativity degree of a group which is the -th power commutativity degree of a group and it is defined as the probability of the -th power of two random elements in a group commute. Some previous studies have been found for  equal to 2 and 3 and both probabilities are called as squared commutativity degree and cubed commutativity degree respectively. In this research, the -th power commutativity degree is determined for  equal to 4, called as quartic commutativity degree and some generalization formulas have been obtained. However, this research focuses only on the dihedral groups.


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