Some projective planes of Lenz-Barlotti class I
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- by John T. Baldwin PDF
- Proc. Amer. Math. Soc. 123 (1995), 251-256 Request permission
Abstract:
We construct an infinite projective plane with Lenz-Barlotti class I. Moreover, the plane is almost strongly minimal in a very strong sense: each automorphism of each line extends uniquely to an automorphism of the plane.References
- John T. Baldwin, An almost strongly minimal non-Desarguesian projective plane, Trans. Amer. Math. Soc. 342 (1994), no. 2, 695–711. MR 1165085, DOI 10.1090/S0002-9947-1994-1165085-8
- C. R. J. Clapham, A. Flockhart, and J. Sheehan, Graphs without four-cycles, J. Graph Theory 13 (1989), no. 1, 29–47. MR 982865, DOI 10.1002/jgt.3190130107
- P. Dembowski, Finite geometries, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 44, Springer-Verlag, Berlin-New York, 1968. MR 0233275, DOI 10.1007/978-3-642-62012-6 E. Hrushovski, Construction of a strongly minimal set, preprint, 1988.
- Daniel R. Hughes and Fred C. Piper, Projective planes, Graduate Texts in Mathematics, Vol. 6, Springer-Verlag, New York-Berlin, 1973. MR 0333959
- Bruno Poizat, Sous-groupes définissables d’un groupe stable, J. Symbolic Logic 46 (1981), no. 1, 137–146 (French). MR 604887, DOI 10.2307/2273265 J. Yaqub, The Lenz-Barlotti classification, Proceedings of the Projective Geometry Conference, 1967 (R. Sandler, ed.), University of Illinois at Chicago Circle, 1967.
Additional Information
- © Copyright 1995 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 123 (1995), 251-256
- MSC: Primary 51A35
- DOI: https://doi.org/10.1090/S0002-9939-1995-1215026-6
- MathSciNet review: 1215026