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Probabilities of Reverse Property on Dihedral Groups |
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| รหัสดีโอไอ | |
| Creator | Kanokporn Changtong |
| Title | Probabilities of Reverse Property on Dihedral Groups |
| Contributor | Wararat Arun |
| Publisher | Faculty of Science, Ubon Ratchathani University |
| Publication Year | 2565 |
| Journal Title | Journal of Science and Science Education |
| Journal Vol. | 5 |
| Journal No. | 2 |
| Page no. | 70-77 |
| Keyword | Probability, dihedral group, reverse property |
| URL Website | https://so04.tci-thaijo.org/index.php/JSSE |
| Website title | Journal of Science and Science Education |
| ISSN | ISSN 2697-410X |
| 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 G by using probability concept. The P_2 (G) 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 D_n where n is a positive integer, and found the general form of P_2 (D_n). Langley, Levitt and Rower (2011) generalized P_2 (G) to P_n (G), where P_n (G) is the probability that a product of n 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 3 group elements in Dihedral groups D_n equal to its reverse, namely P_3 (D_n). |
