# Subplanes of finite projective planes

Let
be a finite projective plane,
and let
be a proper subplane of
.
Let n and m be the order of
and
,
respectively.
**Lemma.**
and m^{2}=n if and only if
is a Baer subplane of
.

Moreover, if
isn't a Baer subplane of
,
we have in fact

Contributed by Hauke Klein

Version `$Id: subfin.html,v 1.1 2001/01/02 19:41:04 hauke Exp $`