On the Isomorphism Classes of Transversals III

Let G be a finite group and H a subgroup of G. Each left transversal (with identity) of H in G has a left loop (left quasigroup with identity) structure induced by the binary operation of G. We say two left transversals are isomorphic if they are isomorphic with respect to the induced left loop structures. In this paper, the number of isomorphism classes of transversals is calculated for some family of pairs (G,H). With the help of this, the number of non-isomorphic left loop of order n has been calculated.