Isotopic Classes of Transversals in Dihedral Group D2n, n Odd

Abstract

In this article we determine the number of isotopic classes of transversals of a subgroup of order 2 in D 2n (n is a positive odd integer greater than 1), where isotopism classes are formed with respect to the induced right loop structures. We also determine the cyclic index of the Affine group Aff(1, p 2 ), where p is an odd prime.