Order classes of dihedral groups

Abstract

The order of an element x in a finite group G is the smallest positive integer k, such that xk is the group identity. The set of all possible such orders joint with the number of elements that each order referred to, is called the order classes of G. The conjugacy classes of dihedral groups already known, the conjugacy classes is a refinement partition to the order classes. In this paper, the order classes of dihedral groups are derived. In addition, clarifications for some cases related to the size of the groups were given. © 2014 AIP Publishing LLC.