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.

Keywords: Projective plane, Ber's subplane.

MSC: 51E15

Pages:  67$-$69     

Volume  46 ,  Issue  3$-$4 ,  1994