Result Details
Links Between HX-Groups and Hypergroups
Cristea Irina, doc. dr., UMAT (FEEC)
Babatunde Oluwaseun Onasaya
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.
HX-group, hyperstructure theory, Chinese hypergroupoid, EL-hyperstructure, power set
@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"
}