CHARACTERIZATION OF POLYGROUPS BY IP-SUBSETS

Abstract

In this paper, we define the concept of IP-subsets of a polygroup and single polygroups. Indeed, if < P, o, 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 is an element of Q, x*y = (x circle y) boolean AND 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.