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Miquelian inversive planes which admit an orthogonality both in the sense of Dembowski and Hughes and of Benz

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Abstract

The object of this article is to prove a necessary and sufficient condition such that the orthogonality defined by Dembowski and Hughes in the case of characteristic different from 2 (see [4]) satisifes the following axiom: Two orthogonal circles are secant.

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References

  1. Benz, W., ‘Über Möbiusebenen’, Ein Bericht, Jahresber. Deutsche Math. Ver. 63 (1960), 1–27.

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  2. Bourbaki, N., ‘Elements de Mathématiques’, Fascicule XXIV, Livre II, Algèbre, Chap. 9, Formes sesquilinéaires et formes quadratiques, Hermann, 1959.

  3. Dembowski, P., Finite Geometries, Springer, Berlin, Heidelberg, New York, 1968.

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  4. Dembowski, P. and Hughes, D. R., ‘On Finite Inversive Planes’, J. London Math. Soc. 40 (1965), 171–182.

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  1. Pécamp bas, Appelle, F-81700, Puylaurens, France

    Yves Mencerrey

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  1. Yves Mencerrey
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Mencerrey, Y. Miquelian inversive planes which admit an orthogonality both in the sense of Dembowski and Hughes and of Benz. Geom Dedicata 27, 199–202 (1988). https://doi.org/10.1007/BF00151350

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  • DOI: https://doi.org/10.1007/BF00151350

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