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A non-symmetric translation plane of order \(17^ 2\). (English) Zbl 0705.51003

Inspired by a recent work of N. L. Johnson [J. Geom. 36, No.1/2, 63-90 (1989; Zbl 0695.51003)] the author proves the existence of a two- dimensional translation plane of order \(17^ 2\), whose full ranslation complement consists of the kernel homologies, and that this translation plane gives rise to \((17^ 2+1)(17+1)\) mutually nonisomorphic strict semi-translation planes of order \(17^ 2\). The reader may find the details in the original paper and the related notation and concepts in the above quoted Johnson’s paper.
Reviewer: G.Faina

MSC:

51A40 Translation planes and spreads in linear incidence geometry
51D20 Combinatorial geometries and geometric closure systems

Citations:

Zbl 0695.51003
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References:

[1] C. Charries, ?An Invariant and some Translation Planes?, submitted.
[2] C. Charnes, Thesis, Cambridge University.
[3] C. Charnes, ?A New Invariant of Projective Planes?, submitted.
[4] J. H. Conway, P. B. Kleidman, and R. A. Wilson, ?New Families of Ovoids inO 8 + ,Geom. Dedicata 26 no. 2 (1988), 152-170. · Zbl 0643.51015 · doi:10.1007/BF00151667
[5] P. Dembowski, Finite Geometries, Springer-Verlag, Berlin, Heidelberg, New York, 1968.
[6] N. L. Johnson, ?The Derivation of Dual Translation Planes?, Journal of Geometry, to appear. · Zbl 0695.51003
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