Department of Mathematics
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It is well-known that projective planes over GF(p) cannot be realized as subplanes of projective planes over GF(q) if p and q are independent. However, the situation in affine planes are very different. Affine planes are not that rigid to characterize their coordinate fields. For example, it is possible to realize the affine plane AG(2,3) as a subplane of projective planes over several fields including those with zero characteristic. Here we employ the computational techniques of resultants of Singer polynomials to realize the various embeddings. This work was done in collaboration with N. S. Mendelosohn and Barry Wolk.

References

1. T. G. Ostrom and F. A. Sherk, Finite projective planes as affine subplanes, Canad. J. Math 34 (1964) 257-297.
2. G. Pickert, Projektive Ebenen, Berlin-Heidelberg-New York, 1985.
3. N.S. Mendelsohn, R. Padmanabhan and B. Wolk, Placement of the Desargues configuration on a cubic curve. Geom. Dedicata 40 (1991) 165--170.