School of Mathematical & Statistical Sciences Faculty Publications and Presentations

On residually thin hypergroups

Document Type

Article

Publication Date

6-2020

Abstract

The notion of a hypergroup (in the sense of [11]) provides a far reaching and meaningful generalization of the concept of a group. Specific classes of hypergroups have given rise to challenging questions and interesting connections to geometric and group theoretic topics; cf. [12], [13], and [15]. In the present article, we investigate residually thin hypergroups, that is hypergroups H which contain closed subsets F 0 , …, F n such that F 0 = { 1 } , F n = H , and, for each element i in { 1 , … , n } , F i − 1 ⊆ F i and F i / / F i − 1 is thin. In our first main result, we analyze the normal structure of residually thin hypergroups. The second main result of this note says that finite hypergroups are residually thin if all of their elements h satisfy h h ⁎ h = { h } . Our investigation, in particular our focus on this latter condition, was inspired by a study of metathin association schemes; cf. [6], [7]. We therefore would like to dedicate this article to Mitsugu Hirasaka who initiated this study.

Comments

© 2020 Elsevier Inc. Under an Elsevier user license http://www.elsevier.com/open-access/userlicense/1.0/

Publication Title

Journal of Algebra

DOI

10.1016/j.jalgebra.2019.12.025

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