Strongly Regular Relations Derived from Fundamental Relation

Abstract

We introduce a new regular relation δ on a given group G and show that δ is a congurence relation on G, with respect to module the commutator subgroup of G. Then we show that the effect of this relation on the fundamental relation β is equal to the fundamental relation γ, and we conclude that, if ρ is an arbitrary strongly regular relation on the hypergroup H, then the effect of δ on ρ, results in a strongly regular relation on H such that its quotient is an abelian group.