Nilpotent groups derived from hypergroups

Engel groups derived from hypergroups

“…The smallest equivalence relation on a hypergroup H such that the quotient H/ω * , the set of all equivalence classes, is an abelian (resp. nilpotent) group was introduced in [8,1]. Now in this paper we introduce and analyze a new strongly regular relation ξ * s on a hypergroup H such that the quotient group H/ξ * s is an Engle group.…”

“…Proof. In [1] it was proved that ν * n ⊆ γ * . Thus it is sufficient to prove that β * ⊆ ξ * n,s ⊆ ν * n .…”

“…In [1] ν n = ∪ m≥1 ν m,n , where ν 1,n is the diagonal relation and for every integer m > 1, ν m,n is the relation defined as follows:…”

(Fuzzy) hyperlattices and fuzzy preordered lattices

“…(2) For a strongly order-preserving homomorphism f , it is enough to prove the set inclusion L µ 2 (f (x)) ⊆ f (L µ 1 (x)) according to (1). Let y ∈ L µ 2 (f (x)), that is, µ 2 (y, f (x)) = 1.…”

“…Recent research work focuses on the fundamental relations in algebraic hyperstructures by which ordinary algebraic structures are derived from corresponding algebraic hyperstructures [1,2,27]. For example, starting from a hyperlattice, Rasouli et al [27] obtain a lattice by the fundamental relation in hyperlattices.…”