×

Locally projective-planar lattices which satisfy the bundle theorem. (English) Zbl 0433.06013


MSC:

06C10 Semimodular lattices, geometric lattices
51B20 Minkowski geometries in nonlinear incidence geometry
PDFBibTeX XMLCite
Full Text: DOI EuDML

References:

[1] Barlotti, A.: Un’estensione del teorema di Segre-Kustaanheimo. Boll. Un. Mat. Ital.10, 248-252 (1955) · Zbl 0066.38901
[2] Benz, W.: Über Möbiusebenen. Ein Bericht. Jber. Deutsch. Math.-Verein.62, 1. Abt., 1-27 (1960) · Zbl 0098.12501
[3] Benz, W., Mäurer, H.: Über die Grundlagen der Laguerre-Geometrie. Ein Bericht. Jber. Deutsch. Math.-Verein.67, 1. Abt., 14-42 (1965) · Zbl 0125.10002
[4] Birkhoff, G.: Lattice Theory, 3rd ed. Providence, Rhode Island: American Mathematical Society 1967 · Zbl 0153.02501
[5] Blaschke, W.: Eine topologische Kennzeichnung der Kreise auf der Kugel. Abh. Math. Sem. Univ. Hamb.3, 164-166 (1924) · JFM 50.0488.02
[6] Bruck, R.H.: Finite nets. II. Uniqueness and imbedding. Pacific J. Math.13, 421-457 (1963) · Zbl 0124.00903
[7] Buekenhout, F.: Characterizations of semi-quadrics: a survey. In: Colloquio Internazionale sulle Teorie Combinatorie, Tomo I (Roma 1973), pp. 393-421. Atti dei Convegni Lincei17, Roma: Accademia Nazionale dei Lincei 1976
[8] Buekenhout, F.: Inversions in locally affine circular spaces, II. Math. Z.120, 165-177 (1971) · Zbl 0207.19403
[9] Chen, Y.: A characterization of some geometries of chains. Canad. J. Math.26, 257-272 (1974) · Zbl 0281.50011
[10] Coxeter, H.S.M.: The Real Projective Plane. Cambridge: Cambridge University Press 1955 · Zbl 0065.36401
[11] Dembowski, P.: Möbiusebenen gerader Ordnung. Math. Ann.157, 179-205 (1964) · Zbl 0137.40103
[12] Dembowski, P.: Finite Geometries. Berlin-Heidelberg-New York: Springer 1968 · Zbl 0159.50001
[13] Dembowski, P., Hughes, D.R.: On finite inversive. planes. J. London Math. Soc.40, 171-182 (1965) · Zbl 0137.14603
[14] Ewald, G.: Beispiel einer Möbiusebene mit nichtisomorphen affinen Unterebenen. Arch. Math. (Basel).11, 146-150 (1960) · Zbl 0095.34703
[15] Heise, W., Karzel, H.: Symmetrische Minkowski-Ebenen. J. Geometry3, 5-20 (1973) · Zbl 0252.50030
[16] Hesselbach, B.: Über zwei Vierecksätze in der Kreisgeometrie. Abh. Math. Sem. Univ. Hamburg.9, 265-271 (1933) · JFM 59.1232.02
[17] Hoffman, A.J.: On the foundations of inversion geometry. Trans. Amer. Math. Soc.71, 218-242 (1951) · Zbl 0044.15504
[18] Kaerlein, G.: Der Satz von Miquel in der pseudo-euklidischen (Minkowskischen) Geometrie. Ph.D. thesis, Bochum (1970)
[19] Kahn, J.: Finite inversive planes satisfying the bundle theorem. Preprint · Zbl 0482.51011
[20] Kahn, J.: Inversive planes satisfying the bundle theorem. J. Combinatorial Theory Ser. A29, 1-19 (1980) · Zbl 0438.51006
[21] Kahn, J.: Locally projective-planar lattices which satisfy the bundle theorem. Ph.D. thesis, Ohio State University (1979) · Zbl 0433.06013
[22] Kantor, W.M.: Dimension and embedding theorems for geometric lattices. J. Combinatorial Theory Ser. A18, 12-26 (1975) · Zbl 0312.05018
[23] Mäurer, H.: Ein axiomatischer Aufbau der mindestens 3-dimensionalen Möbius-Geometrie. Math. Z.103, 282-305 (1968) · Zbl 0156.40804
[24] Segre, B.: Ovals in a finite projective plane. Canad. J. Math.7, 414-416 (1955) · Zbl 0065.13402
[25] Segre, B.: On complete caps and ovaloids in three-dimensional Galois spaces of characteristic two. Acta. Arith.5, 315-332 (1959) · Zbl 0094.15902
[26] Tits, J.: Ovoïdes à translations. Rend. Mat.21, 37-59 (1962) · Zbl 0107.38103
[27] Tits, J.: Ovoïdes et groups de Suzuki. Arch. Math. (Basel)13, 187-198 (1962) · Zbl 0109.39402
[28] van der Waerden, B.L., Smid, L.J.: Eine Axiomatik der Kreisgeometrie und der Laguerre-Geometrie. Math. Ann.110, 753-776 (1935) · Zbl 0010.26803
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.