Set of involutions arising from an egglike inversive plane (Q1879090)

An ovoid of PG\((3,n)\), \(n>2\), is a set of \(n^2+1\) points, no three of which are collinear. Every plane of PG\((3,n)\) intersects an ovoid in \(n+1\) or one point. They are examples of inversive planes, i.e., 3-\((n^2+1,n+1,1)\)-designs, also called egglike inversive planes. To any ovoid of PG\((3,n)\), a family of involutions is associated in a natural way. \textit{G. Korchmáros} and \textit{D. Olanda} [J. Geom. 21, 53-58 (1983; Zbl 0527.51005)] investigated the properties of a family of involutions of \(n^2+1\) points to ensure that they correspond to an inversive plane. They defined four properties for such a family of involutions, and showed that they were sufficient to make this family of involutions define an ovoid, i.e., an egglike inversive plane. The authors give in this article a new proof of this result, explicitly constructing the Galois space PG\((3,n)\), in which the ovoid is embedded. To achieve this goal, they use ideas of finite linear spaces.