Publication detail

Links Between HX-Groups and Hypergroups

NOVÁK, M. CRISTEA, I. BABATUNDE OLUWASEUN, O.

Original Title

Links Between HX-Groups and Hypergroups

Type

journal article in Web of Science

Language

English

Original Abstract

The concept of an HX-group is an upgrade of the concept of a group, in which a new operation is defined on the family of non-empty subsets of a group. If this new support set together with the new operation is a group, then we call it an HX-group. On the other hand, a hyperoperation is a mapping having the same codomain as the operation of an HX-group, i.e., the family of non-empty subsets of the initial set, but a different domain — the set itself. This could be (and was indeed) a source of confusion, which is clarified in this paper. Moreover, HX-groups naturally lead to constructions of hypergroups. The links between these two algebraic concepts are presented, with the aim of reviving the old notion of an HX-group in the current research on algebraic hyperstructures. One of such existing links and one newly established link are also discussed.

Keywords

HX-group, hyperstructure theory, Chinese hypergroupoid, EL-hyperstructure, power set

Authors

NOVÁK, M.; CRISTEA, I.; BABATUNDE OLUWASEUN, O.

Released

28. 7. 2021

Publisher

World Scientific

ISBN

1005-3867

Periodical

ALGEBRA COLLOQUIUM

Year of study

28

Number

3

State

People's Republic of China

Pages from

441

Pages to

452

Pages count

12

URL

https://www.worldscientific.com/doi/epdf/10.1142/S1005386721000341

BibTex

@article{BUT172123,
  author="Michal {Novák} and Irina {Cristea} and Onasaya {Babatunde Oluwaseun}",
  title="Links Between HX-Groups and Hypergroups",
  journal="ALGEBRA COLLOQUIUM",
  year="2021",
  volume="28",
  number="3",
  pages="441--452",
  doi="10.1142/S1005386721000341",
  issn="1005-3867",
  url="https://www.worldscientific.com/doi/epdf/10.1142/S1005386721000341"
}