On the Isomorphism Classes of Transversals

Abstract

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

Key Words:

• Minimal counter example
• Right quasigroup
• Transversals

2000 Mathematics Subject Classification:

• 20D60
• 20N05

ACKNOWLEDGMENTS

The authors wish to thank the referee for giving useful comments for improvement and completing some arguments of the article.

The first author is supported by UGC, Government of India.

Notes

Communicated by H. D. Macpherson