Probabilities of Reverse Property on Dihedral Groups

Main Article Content

Kanokporn Changtong
Wararat Arun

Abstract

It is well-known that one of the important group properties is commutativity. We are investigating how far a non-abelian group from commutativity. Gallian (2010) described a way to measure the commutativity of a finite group by using probability concept. The  is defined as the probability that two randomly selected elements of the group actually commute. Later, Clifton, Guichard and Keef (2011) studied this probability on the dihedral group  where  is a positive integer, and found the general form of . Langley, Levitt and Rower (2011) generalized  to , where  is the probability that a product of  group elements equal to its reverse. The objectives of this research is to understand these probabilities and we found the general form of the probability that a product of  group elements in Dihedral groups  equal to its reverse, namely .

Article Details

How to Cite
Changtong, K. ., & Arun, W. . (2022). Probabilities of Reverse Property on Dihedral Groups. Journal of Science and Science Education (JSSE), 5(2), 241–248. https://doi.org/10.14456/jsse.2022.28 (Original work published June 27, 2022)
Section
Research Articles in Science

References

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