THE SQUARED COMMUTATIVITY DEGREE OF DIHEDRAL GROUPS
DOI:
https://doi.org/10.11113/jt.v78.7811Keywords:
Commutativity degree, Dihedral group, finite groupAbstract
The commutativity degree of a finite group is the probability that a random pair of elements in the group commute. Furthermore, the n-th power commutativity degree of a group is a generalization of the commutativity degree of a group which is defined as the probability that the n-th power of a random pair of elements in the group commute. In this paper, the n-th power commutativity degree for some dihedral groups is computed for the case n equal to 2, called the squared commutativity degree.References
Miller, G.1944. A Relative Number of Non-Invariant Operators in a Group, Proc. Nat. Acad. Sci.USA. 25-28.
Erdos, P. and Turan, P. 1968. On Some Problems of a Statistical Group Theory. IV, Acta Math. Acad Sci. Hungaricae. 19:413-435.
Mohd Ali, N. M. and Sarmin, N. H. 2010. On Some Problems in Group Theory of Probabilistic Nature. Menemui Matematik (Discovering Mathematics). 32(2):35-41.
Erfanian, A., Tolue, B. and Sarmin, N. H. 2011. Some Considerations on the n-th Commutativity Degree. Ars Combinatorial Journal. 3:495-506.
Dummit, D. S. and Foote, R. M. 2014. Abstract Algebra, Third Edition. John Wiley and Son, USA. 2004.
Mashkouri, M. and Taeri. B. 2011. On a Graph Associated to Groups. Bulletin of The Malaysian Mathematical Sciences Society. 34(3):553-560.
Downloads
Issue
Section
License
Copyright of articles that appear in Jurnal Teknologi belongs exclusively to Penerbit Universiti Teknologi Malaysia (Penerbit UTM Press). This copyright covers the rights to reproduce the article, including reprints, electronic reproductions, or any other reproductions of similar nature.
