Fadila Normahia Abd. Manaf

Relative commutativity degree of some dihedral groups

The commutativity degree of a finite group G was introduced by Erdos and Turan for symmetric groups, finite groups and finite rings in 1968. The commutativity degree, P(G), is defined as the probability that a random pair of elements in a group commute. The relative commutativity degree of a group G is defined as the probability for an element of subgroup, H and an element of G to commute with one another and denoted by P(H,G). In this research the relative commutativity degree of some dihedral groups are determined.

A general case of the commutativity degree of nilpotent p-groups of class two

Given a finite group, the commutativity degree of the group is defined as the probability that two elements of the group, chosen randomly with replacement, commute. The commutativity degree can be considered as a special case of a more general probability which is the probability that the commutator of two group elements is equal to a given element in the group. This research focuses on the finite p-groups of nilpotency class two. Some basic concepts and results on the general case of the commutativity degree are presented.