Suppose that M is embedded into a Desarguesian projective space B.
Neither [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] can be embedded into a Desarguesian projective space.
which can be realized in a (Desarguesian) projective space seems natural.
As a rule, in the sequel we consider only embeddings into Desarguesian spaces.
* Show there exist semifield planes of order [2.sup.r], for any odd integer r that admit Desarguesian subplanes of order [2.sup.2].
To illustrate the complexity of the situation, recall again that there are semifield planes of order 25 that contain semifield subplanes of order [2.sup.2], necessarily Desarguesian and there are semifields planes of orders [2.sup.5k] or [2.sup.7k], for k odd, that admit Desarguesian subplanes of order 22.
(2) The transposed then dualized commutative binary Knuth semifield planes of order [2.sup.n] for n = 5k, or 7k, for k odd, are symplectic and admit Desarguesian subplanes of orders [2.sup.2].
Every commutative binary Knuth semifield plane of order [2.sup.5k] or [2.sup.7k], for k odd, admits a Desarguesian subplane of order 4.