Strongly Regular Relations Derived from Fundamental Relation

Document Type : Original Article


1 Department of Mathematics, Statistics and Computer Science, Faculty of Science, University of Tehran, Tehran, Iran.

2 School of Mathematics, Statistic and Computer Sciences, Tehran, Iran.


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.


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