Probabilities of Reverse Property on Dihedral Groups
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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 .
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