## Related pagesSubplanes of finite projective planesThe small projective planes |

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If q is a prime power, then the projective plane over GF(q) is a finite projective plane of order q. In fact, all known finite projective planes are of prime power order. Unfortunately, there is only one known theorem excluding a great range of values for the order n, namely the Bruck-Ryser theorem. The following things are commonly conjectured.

**Conjecture.**The order of a finite projective plane is always a prime power.**Conjecture.**A finite projective plane of prime order is Desarguesian.

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