Isotopic classes of transversals in Dihedral group $ D_{2n} $, $n$ odd

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.