Non-commutative hypergroup of order five-Reference-Cited by-同舟云学术

Non-commutative hypergroup of order five

Published:2016-06-30 Issue:07 Volume:16 Page:1750127
ISSN:0219-4988
Container-title:Journal of Algebra and Its Applications
language:en
Short-container-title:J. Algebra Appl.

Author:

Matsuzawa Yasumichi¹,Ohno Hiromichi²,Suzuki Akito²,Tsurii Tatsuya³,Yamanaka Satoe⁴

Affiliation:

1. Department of Mathematics, Faculty of Education, Shinshu University, 6-Ro, Nishi-nagano, Nagano 380-8544, Japan

2. Department of Mathematics, Faculty of Engineering, Shinshu University, 4-17-1 Wakasato, Nagano 380-8553, Japan

3. Graduate School of Science of the Osaka Prefecture University, 1-1 Gakuen-cho, Nakaku, Sakai, Osaka 599-8531, Japan

4. Faculty of Science, Nara Women’s University, Kitauoyahigashimachi, Nara 630-8506, Japan

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.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Algebra and Number Theory

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0219498817501274

Reference19 articles.

1. Harmonic Analysis of Probability Measures on Hypergroups

2. A cohomology approach to the extension problem for commutative hypergroups

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