# On the number of isomorphism classes of quasigroups

## TL;DR

This paper calculates the number of isomorphism classes of right transversals of symmetric groups, providing a foundation for further classification of subgroups based on transversal isomorphism classes.

## Contribution

It introduces a method to determine the count of isomorphism classes of right transversals in symmetric groups, advancing subgroup classification techniques.

## Key findings

- Number of isomorphism classes of right transversals of _{n-1} in _n calculated
- Methodology applicable to subgroup classification problems
- Potential for extending classification of subgroups with specific transversal properties

## 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.