in this paper using strongly duplexes we introduce a new class of (semi)hypergroups. the associated (semi)hypergroup from a strongly duplex is called duplex (semi)hypergroup. two computer programs written in matlab show that the two groups $z_{2n}$ and $z_{n}times z_{2}$ produce a strongly duplex and its associated hypergroup is a complementary feasible hypergroup.

This paper gives a complete classification of the finite groups that contain a strongly closed p-subgroup for p any prime.

We characterise strongly minimal groups interpretable in elementary extensions of compact complex analytic spaces.

We derive strong structural constraints on the automorphism groups of strongly regular (s. r.) graphs, giving a surprisingly strong answer to a decades-old problem, with tantalizing implications to testing isomorphism of s. r. graphs, and raising new combinatorial challenges. S. r. graphs, while not believed to be Graph Isomorphism (GI) complete, have long been recognized as hard cases for GI, ...

In this paper using strongly duplexes we introduce a new class of (semi)hypergroups. The associated (semi)hypergroup from a strongly duplex is called duplex (semi)hypergroup. Two computer programs written in MATLAB show that the two groups $Z_{2n}$ and $Z_{n}times Z_{2}$ produce a strongly duplex and its associated hypergroup is a complementary feasible hypergroup.

Let U be either the universal enveloping algebra of a complex semisimple Lie algebra g or its Drinfel’d-Jimbo quantisation over the field C(z) of rational functions in the indeterminate z. We define the notion of “strongly multiplicity free” (smf) for a finite dimensional U-module V , and prove that for such modules the endomorphism algebras EndU (V ⊗r) are “generic” in the sense that they are ...

Strongly dependent ordered abelian groups have finite dprank. They are precisely those groups with finite spines and |{p prime : [G : pG] = ∞}| < ∞. We apply this to show that if K is a strongly dependent field, then (K, v) is strongly dependent for any henselian valuation v and the value group and residue field are stably embedded as pure structures.

Minimal, strongly proximal actions of locally compact groups on compact spaces, also known as boundary actions, were introduced by Furstenberg in the study of Lie groups. In particular, the action of a semi-simple real Lie group G on homogeneous spaces G/Q where Q ⊂ G is a parabolic subgroup, are boundary actions. Countable discrete groups admit a wide variety of boundary actions. In this note ...