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

9 pages