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چکیده
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In this paper, we define the concept of IP-subsets of a polygroup and single polygroups. Indeed, if ⟨P,∘,1,−1⟩ is a polygroup of order n, then a non-empty subset Q of P is an IP-subset if ⟨Q,∗,e,I⟩ is a polygroup, where for every x,y∈Q, x∗y=(x∘y)∩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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