Probabilities of Reverse Property on Dihedral Groups
Article Sidebar
Main Article Content
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
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
The Journal of Science and Science Education (JSSE) retain the right of all articles published in JSSE. The coresponding author or the authorized person on behalf of the authors must send the complete Copyright Transfer Form to JSSE before any article get published in JSSE.
Copyright Transfer Form
The JSSE request the coresponding author or the authorized person on behalf of the authors upload the manuscript under the together with the Copyright Transfer Form under the supplementary data. The guidline for uploading both manuscript and Copyright Transfer Form is shown below:
1. Upload the manuscript in the sub-menu, Article Component > Article Text.
2. Upload the the Copyright Transfer Form in the sub-menu, Article Component > Other.
Download Copyright Transfer Form
References
Clifton, C., Guichard, D. and Keef, P. (2011). How commutative are direct products of Dihedral groups.
Mathematics Magazine, 84, 137-140.
Gallian, J. (2010). Contemporary Abstract Algebra (7th ed). Belmont, CA: Brooks Cole.
Langley, T., Levitt, D. and Rower, J. (2011). Two generalizations of 5/8 bound on commutativity in
nonabelian finite groups. Mathematics Magazine, 84, 128-136.
Nicholson, W. K., (2012). Introduction to Abstract Algebra (4th ed). New Jersey: Wiley.
Rotman, J. J. (1996). A first Course in Abstract Algebra. New Jersey: Prentice Hall.
Sherman, G.J. (1997). Trying to do group theory with undergraduates and computers. Journal of Symbolic
Computation.23, 577-587.