## Related pagesInvolutorial collineationsSubplanes of finite projective planes |

- Given any point there exists exactly one line through p.
- Given any line there exists exactly one point on l.

**Lemma.** Let
be a subplane
of a projective plane
.
Let (o,e,u,v) be a quadrangle contained in the given subplane and
let (K,T) be the corresponding ternary field.
Then
is a subfield of (K,T).
The subplane
is a Baer subplane of
if and only if the following three conditions hold.

- .
- .
- .

**Lemma.** Let V be a three-dimensional vector space over a skewfield K.
Let
be a subplane of PG(V). Then there exist
a subskewfield P of K and a basis e_{1},e_{2},e_{3}
of V such that
The subplane
is a Baer subplane if and only if K is of dimension 2 over P as a
left vector space and as a right vector space, respectively.

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