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ЖУРНАЛЫ // Eurasian Mathematical Journal // Архив

Eurasian Math. J., 2020, том 11, номер 3, страницы 35–41 (Mi emj372)

Characterization of polygroups by IP-subsets

D. Heidaria, B. Davvazb

a Faculty of Science, Mahallat Institute of Higher Education, 1 Km. of Khomein Road, P.O. Box 37811-51958, Mahallat, Iran
b Department of Mathematics, Yazd University, University Blvd , Safayieh, P.O. Box 89195-741, Yazd, Iran

Аннотация: In this paper, we define the concept of IP-subsets of a polygroup and single polygroups. Indeed, if $\langle P,\circ,1,{}^{-1} \rangle$ is a polygroup of order $n$, then a non-empty subset $Q$ of $P$ is an IP-subset if $\langle Q,*,e,{}^I \rangle$ is a polygroup, where for every $x, y\in Q$, $x*y=(x\circ y)\cap Q$. If $P$ has no IP-subset of order $n-1$, then it is single. We show that every non-single polygroup of order $n$ can be constructed from a polygroup of order $n-1$. In particular, we prove that there exist exactly $7$ single polygroups of order less than $5$.

Ключевые слова и фразы: hypergroup, polygroup, IP-subset, single polygroup.

MSC: 20N20

Поступила в редакцию: 11.06.2019

Язык публикации: английский

DOI: 10.32523/2077-9879-2020-11-3-35-41



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