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To every egglike inversive plane there is associated a family F ( ) of involutions of the point set of such that circles of are the fixed point sets of the involutions in F ( ). Korchmaros and Olanda characterized a family F of involutions on a set of size n 2 + 1 to be F ( ) for an egglike inversive plane of order n by four conditions. In this paper, we give an alternative proof where the Galois space P G(3, n) in which is embedded is built up directly by using concepts and results on finite linear spaces. (2000): 05B25, 51A45. Mathematics Subject Classification