Geodesic
Characterization of polygroups by IP-subsets
Eurasian mathematical journal, Tome 11 (2020) no. 3, pp. 35-41.

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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 $5$. 
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D. Heidari; B. Davvaz. Characterization of polygroups by IP-subsets. Eurasian mathematical journal, Tome 11 (2020) no. 3, pp. 35-41. http://geodesic.mathdoc.fr/item/EMJ_2020_11_3_a2/

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