Abstract
The ϰ-affine space is defined, i.e. a geometry in which ϰ distinct points are joint by exactly one ‘curve’ (subspace of dimension 1). This definition generalizes the notions of affine [1] and Möbius [4] spaces. An example of a 5-affine space with the Mathieu group\(\mathfrak{M}_{12}\) as automorphism group is constructed. There are only a few models of at least 4-affine planes of finite order.
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Literatur
BUEKENHOUT, F.: Une caractérisation des espaces affines basée sur la notion de droite. Math. Z.111, 367–371 (1969).
DEMBOWSKI, P.: Möbiusebenen gerader Ordnung. Math. Ann.157, 179–205 (1964).
DEMBOWSKI, P.: Finite geometries. Berlin-Heidelberg-New York: Springer 1968.
HEISE, W.: Eine Definition des Möbiusraumes. manuscr. math.2, 39–47 (1970).
HUGHES, D. R.: On t-designs and groups. Amer. J. Math.87, 761–778 (1965).
KARZEL, H. und I. PIEPER: Bericht über geschlitzte Inzidenzgruppen. Ersch. demnächst Jber, dtsch. Math.-Ver.
WITT, E.: Die 5-fach transitiven Gruppen von Mathieu. Abh. Hamburg12, 256–264 (1938).
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Heise, W., Timm, J. ϰ-affine Räume. Manuscripta Math 4, 31–37 (1971). https://doi.org/10.1007/BF01168903
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DOI: https://doi.org/10.1007/BF01168903