Some discussions related to disjoint Ber's subplanes

Abstract

A projective plane $\Cal P_m$ is a Ber's subplane of a finite projective plane $\Cal P_n$ if every point and line of $\Cal P_n\setminus\Cal P_m$ is incident to some line and some point, respectively, of $\Cal P_n$. It is known that the order of the plane $\Cal P_n$ and its Ber's subplane $\Cal P_m$ satisfy the equation $n=m^2$. In this article we prove some properties of finite projective planes $\Cal P_n$ having disjoint Ber's subplanes covering it.