On the number of isomorphism classes of quasigroups

Abstract

In this paper the number of isomorphism classes of the right transversals of the symmetric group $\Sigma_{n-1}$ in the symmetric group $\Sigma_n$ is calculated. This result together with the techniques employed along the paper may be used to go forward in the study and classification of the subgroups with a certain number of isomorphism classes of transversals in the group.