On Frobenius groups of order q(q – 1)

Abstract

In this article, we consider a Frobenius group G of order q(q – 1) whose Frobenius complement H is of order q, where q is a prime power. In this case, right loop structures on right transversals to H in G determine new kinds of algebraic structures termed as generalised right near domains and right near domains respectively. We also determine a reasonable lower bound of their non-isomorphic classes (with their explicit structures). In last section, we gave an idea of public key exchange protocol for right near domains.

Keywords:

• Near domains
• c-groupoids
• General extensions

Mathematics Subject Classification 2010:

• 94A60
• 68P25
• 20N05