Set of involutions arising from an egglike inversive plane

Abstract.

To every egglike inversive plane $\Omega$ there is associated a family $\mathcal{F}(\Omega)$ of involutions of the point set of $\Omega$ such that circles of $\Omega$ are the fixed point sets of the involutions in $\mathcal{F}(\Omega)$. Korchmaros and Olanda characterized a family $\Omega$ of involutions on a set of size n ² + 1to be $\mathcal{F}(\Omega)$ for an egglike inversive plane of order n by four conditions. In this paper, we give an alternative proof where the Galois space PG(3,n) in which $\Omega$ is embedded is built up directly by using concepts and results on finite linear spaces.