Non-commutative hypergroup of order five

Akito Suzuki; Hiromichi Ohno; Satoe Yamanaka; Tatsuya Tsurii; Yasumichi Matsuzawa

arxiv: 1511.06486 · v1 · pith:BEH4PPXWnew · submitted 2015-11-20 · 🧮 math.GR · math.OA

Non-commutative hypergroup of order five

Yasumichi Matsuzawa , Hiromichi Ohno , Akito Suzuki , Tatsuya Tsurii , Satoe Yamanaka This is my paper

classification 🧮 math.GR math.OA

keywords orderfivenon-commutativehypergrouphypergroupsminimumcommutativeeven

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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.

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Non-commutative hypergroup of order five

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