Non-commutative hypergroup of order five
Yasumichi Matsuzawa, Hiromichi Ohno, Akito Suzuki, Tatsuya Tsurii,, Satoe Yamanaka
TL;DR
This paper establishes that all hypergroups of order four are commutative, and demonstrates the existence of a non-commutative hypergroup of order five, highlighting a key difference from groups.
Contribution
It proves that the smallest non-commutative hypergroup has order five, unlike groups where it is six, revealing new structural insights.
Findings
All hypergroups of order four are commutative
Existence of a non-commutative hypergroup of order five
Minimum order of non-commutative hypergroups is five
Abstract
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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Taxonomy
TopicsFinite Group Theory Research · Rings, Modules, and Algebras · Advanced Topics in Algebra