Solvable Polygroups and Derived Subpolygroups

Aghabozorgi, H.; Davvaz, Bijan; Jafarpour, M.

doi:10.1080/00927872.2012.661006

Cited by 16 publications

(8 citation statements)

References 12 publications

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“…Then, by (1) Proof If x ∈ U k and y ∈ U t , then x • y ⊆ U k+t and x −1 ∈ (U −1 ) k = U k , for every k, t ∈ N. Hence, L is a subpolygroup of P. By Theorem 3.4, L is open and closed.…”

Section: Theorem 35 Let P Be a Topological Polygroup Such That Everymentioning

confidence: 88%

“…Till now, only a few papers treated the notion of topological hyperstructures, in the classical and fuzzy case, see [2,7,8,14,16]. Let (H 1 • an isomorphism if it is a homomorphism, and its inverse f −1 is a homomorphism, too.…”

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confidence: 99%

“…For more details about polygroups we refer to [1,9,10,18]. Now, we recall the definition of a topological group from [15].…”

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confidence: 99%

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Topological Polygroups

Heidari

Davvaz

Modarres

2015

Bull. Malays. Math. Sci. Soc.

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This paper deals with certain algebraic systems called polygroups. A polygroup is a completely regular, reversible in itself hypergroup. The concept of topological polygroups is a generalization of the concept of topological groups. In this paper, we present the concept of topological hypergroups and prove some properties. Then, we define the notion of topological polygroups. By considering the relative topology on subpolygroups we prove some properties of them. Finally, the topological isomorphism theorems of topological polygroups are proved.

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Section: Theorem 35 Let P Be a Topological Polygroup Such That Everymentioning

confidence: 88%

mentioning

confidence: 99%

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Topological Polygroups

Heidari

Davvaz

Modarres

2015

Bull. Malays. Math. Sci. Soc.

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“…1.3.2 group, a cyclic group, a solvable group or a nilpotent group. In order to see the answers of these question we refer the readers to [4,5,45,52,62].…”

Section: Fundamental Relations On Hyperstructuresmentioning

confidence: 99%

A brief survey on algebraic hyperstructures: Theory and applications

Davvaz

2020

JAHLA

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I am working on algebraic hyperstructures from 1995. During the last twenty years, I together with my students and co-authors studied and developed the theory of algebraic hyperstructures in many directions. In particular, we tried to find real examples of hyperstructures in nature. In this paper we review some parts of these works such as (1) Fundamental relations on hyperstructures; (2) Fuzzy sets and hyperstructures; (3) Rough sets and hyperstructures; (4) Topology and hyperstructures; (5) Number theory and hyperstructures; (6) n-ary hypergroups and there extension to hyperrings and hypermodules; (7) Applications of hyperstructures in biology, physics and chemistry.

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“…J. Jun also applied an idea of hyperstructures to generalize the definition of valuations in [24]. Some other connections of algebraic geometry over hyperstructures can be find in [3,6,17,22,23,30].…”

Section: Introductionmentioning

confidence: 99%

On geometric polygroups

Arabpur

Jafarpour

Aminizadeh

et al. 2020

Analele Universitatii "Ovidius" Constanta - Seria Matematica

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In this paper, we introduce a geodesic metric space called generalized Cayley graph (gCay(P,S)) on a finitely generated polygroup. We define a hyperaction of polygroup on gCayley graph and give some properties of this hyperaction. We show that gCayley graphs of a polygroup by two different generators are quasi-isometric. Finally, we express a connection between finitely generated polygroups and geodesic metric spaces.

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Solvable Polygroups and Derived Subpolygroups

Cited by 16 publications

References 12 publications

Topological Polygroups

Topological Polygroups

A brief survey on algebraic hyperstructures: Theory and applications

On geometric polygroups

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