On the Number of Isomorphism Classes of Transversals

TL;DR

This paper proves that for any subgroup of a finite group, the number of isomorphism classes of normalized right transversals cannot be exactly four, establishing a specific limitation in group theory.

Contribution

It establishes a new non-existence result regarding the number of isomorphism classes of transversals in finite groups.

Findings

No subgroup of a finite group has exactly four isomorphism classes of normalized right transversals.

The result narrows the possible counts of such classes in finite group structures.

Abstract

In this paper we prove that there does not exist a subgroup $H$ of a finite group $G$ such that the number of isomorphism classes of normalized right transversals of $H$ in $G$ is four.