On the Number of Isomorphism Classes of Transversals
Vipul Kakkar, R. P. Shukla

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 of a finite group such that the number of isomorphism classes of normalized right transversals of in is four.
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Taxonomy
TopicsFinite Group Theory Research · Coding theory and cryptography · graph theory and CDMA systems
