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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.

proceedings of the national academy of sciences, india. section a, physical sciences/proceedings of the national academy of sciences, india, section a, physical sciences

Isotopic Classes of Transversals in Dihedral Group D2n, n Odd