We show that the sum of two adjoint orbits in the Lie algebra of an exponential Lie group coincides with the Campbell-Baker-Hausdorff product of these two orbits. Introduction N. Wildberger and others have recently investigated the structure of the hypergroup of the adjoint orbits in relation with the class hypergroup of compact Lie groups. A generalization of the notion of this type of hypergr...

We generalize the concept of topological hypergroup to Hv-group and define some topologies on Hv-groups by using geometric space, which was defined Freni. By applying these topologies, we have always a without need any more conditions. Moreover, state conditions that make it complete. Our aim is via considering characteristics induced space.

We introduce and study the construction of commutative fundamental relation in fuzzy hypersemigroups and investigate its basic properties. We will determine some necessary and sufficient conditions so that this relation is transitive in fuzzy hypersemigroups. Also we show that this relation is transitive in every fuzzy hypergroup.

In this paper, we first define the notion of a complete general fuzzyautomaton with threshold c and construct an $H_{nu}$- group, as well as commutativehypergroups, on the set of states of a complete general fuzzy automatonwith threshold c. We then define invertible general fuzzy automata, discussthe notions of “homogeneity, “separation, “thresholdness connected, “thresholdnessinner irreducible...

Hypergroups can be subdivided into two large classes: those whose heart coincide with the entire hypergroup and in which is a proper sub-hypergroup. The latter class includes family of 1-hypergroups, reduces to singleton, therefore trivial group. However, very little known about hypergroups that are neither 1-hypergroups nor belong first class. goal this work take step classifying G-hypergroups...