Theses and Dissertations

Date of Award

5-2016

Document Type

Thesis

Degree Name

Master of Science (MS)

Department

Mathematics

First Advisor

Dr. Paul-Hermann Zieschang

Second Advisor

Dr. Elena Poletaeva

Third Advisor

Dr. Jacob A. White

Abstract

This thesis surveys recent results on hypergroups as defined by Frédéric Marty in [3] and [4] and their relation to association schemes as presented in [5]. We show that every association scheme is a hypergroup. Then, we compile a few general results on hypergroups needed for our investigation of hypergroups with three, four and six elements. From [1] and [7], we give examples of hypergroups that do not come from finite schemes and from no scheme at all. Our main result occurs when considering hypergroups S with six elements that have a non-normal closed subset T of order 2 with three cosets. Since such class of hypergroups is too large to be completely described, we investigate a subclass S determined in [7]. We found that at least four hypergroups in this class come from finite schemes. For such purposes, we use the Hanaki-Miyamoto Classification of Small Association Schemes; cf. [8].

Comments

Copyright 2016 Jordy C. Lopez. All Rights Reserved.

https://www.proquest.com/dissertations-theses/on-hypergroups-order-at-most-6/docview/1810996022/se-2?accountid=7119

Download

Included in

Mathematics Commons

Share

COinS