14 research outputs found
Non-commutative hypergroup of order five
We prove that all hypergroups of order four are commutative and that there
exists a non-comutative hypergroup of order five. These facts imply that the
minimum order of non-commutative hypergroups is five even though the minimum
order of non-commutative groups is six
Non-commutative hypergroup of order five
We prove that all hypergroups of order four are commutative and that there exists a non-comutative hypergroup of order five. These facts imply that the minimum order of non-commutative hypergroups is five, even though the minimum order of non-commutative groups is six.ArticleJournal of Algebra and Its Applications.16(7):1750127(2016)journal articl
Extensions of Hypergroups of Order Two by Locally Compact Abelian Groups
The purpose of the present paper is to investigate extension problem in the category of commutative hypergroups. In fact, we determine all extensions of hypergroups of order two by locally compact abelian groups. (AMS Subject Classification : 43A62, 20N20.