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A note on the Figueroa planes. (English) Zbl 0532.51009

R. Figueroa [Math. Z. 181, 471-479 (1982; Zbl 0477.51009)] and C. Hering and H.-J. Schaeffer [Lecture Notes Math. 969, 187-190 (1982; Zbl 0498.51009)] constructed nondesarguesian projective planes of order \(q^ 3\) which contain a subplane of order \(q\) such that the full automorphism group induces \(P\Gamma L(3,q)\) on the subplane. It is pointed out that this construction also works for infinite planes.

MSC:

51E15 Finite affine and projective planes (geometric aspects)
51A35 Non-Desarguesian affine and projective planes
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References:

[1] R. Figueroa, A family of not (V, l)-transitive projective planes of orderq 3, ? 1 (mod3) andq>2. Math. Z.181, 471-479 (1982). · Zbl 0486.51011 · doi:10.1007/BF01182385
[2] C. Hering andH.-J. Schaeffer, On the new projective planes of R. Figueroa; Combinatorial theory. LNM969, 187-190, Berlin-Heidelberg-New York 1982. · Zbl 0498.51009
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