Theses and Dissertations
Date of Award
Master of Science (MS)
Dr. Paul-Hermann Zieschang
Dr. Elena Poletaeva
Dr. Jacob A. White
This thesis surveys recent results on hypergroups as defined by Frédéric Marty in  and  and their relation to association schemes as presented in . 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  and , 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 . 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. .
Lopez, Jordy C., "On hypergroups of order at most 6" (2016). Theses and Dissertations. 58.
Copyright 2016 Jordy C. Lopez. All Rights Reserved.