Multiplicative degree of some dihedral groups

• Main Authors: Rhani, N. A., Ali, N. M. M., Sarmin, N. H., Erfanian, A., Hamid, M. A.
• Format: Conference or Workshop Item
• Published: American Institute of Physics Inc. 2016
• Subjects: QA Mathematics
• Online Access: http://eprints.utm.my/id/eprint/73222/; https://www.scopus.com/inward/record.uri?eid=2-s2.0-84984567391&doi=10.1063%2f1.4954591&partnerID=40&md5=dd54350c1fe1a3cfdf1c1fae66346b1f

Let G be a group and H any subgroup of G. The commutativity degree of a finite group G is defined as the probability that a pair of elements x and y, chosen randomly from a group G, commute. The concept of commutativity degree has been extended to the relative commutativity degree of a subgroup H, which is defined as the probability that a random element of a subgroup, H commutes with another random element of a group G. This research extends the concept of relative commutativity degree to the multiplicative degree of a group G, which is defined as the probability that the product of a pair of elements x, y chosen randomly from a group G, is in H. This research focuses on some dihedral groups.