论文信息 - On Flat Flag-Transitive c.c*-Geometries

On Flat Flag-Transitive c.c*-Geometries

We study flat flag-transitive c.c*-geometries. We prove that, apart from one exception related to Sym(6), all these geometries are gluings in the meaning of [6]. They are obtained by gluing two copies of an affine space over GF(2). There are several ways of gluing two copies of the n-dimensional affine space over GF(2). In one way, which deserves to be called the canonical one, we get a geometry with automorphism group G = 22n· Ln(2) and covered by the truncated Coxeter complex of type D2n. The non-canonical ways give us geometries with smaller automorphism group (G ≤ 22n· (2n−1)n) and which seldom (never ?) can be obtained as quotients of truncated Coxeter complexes.

Antonio Pasini | Barbara Baumeister | A. Pasini | B. Baumeister

[1] Zvonimir Janko,et al. Two New Semibiplanes , 1982, J. Comb. Theory, Ser. A.

[2] Peter J. Cameron,et al. On Groups of Degree N AND n−1, and Highly‐Symmetric Edge Colourings , 1975 .

[3] P. Cameron,et al. One‐Factorizations of Complete Graphs with a Doubly Transitive Automorphism Group , 1993 .

[4] D. Koenig. Theorie Der Endlichen Und Unendlichen Graphen , 1965 .

[5] Martin W. Liebeck,et al. The Affine Permutation Groups of Rank Three , 1987 .

[6] F. Buekenhout,et al. Parallelism in diagram geometry , 1994 .

[7] J. Conway,et al. ATLAS of Finite Groups , 1985 .

[8] B. Baumeister. On flag-transitive c.c* -geometries , 1996 .

[9] Luigi A. Rosati,et al. Buildings and the Geometry of Diagrams , 1986 .

[10] Francis Buekenhout,et al. The geometry of the finite simple groups , 1986 .

[11] Daniel Hughes. Biplanes and semi-biplanes , 1978 .

[12] P. Cameron. FINITE PERMUTATION GROUPS AND FINITE SIMPLE GROUPS , 1981 .

[13] Alan Hartman,et al. Cyclic One-Factorization of the Complete Graph , 1985, Eur. J. Comb..

[14] Christiane Lefèvre-Percsy,et al. Finite rank 3 geometries with affine planes and dual affine point residues , 1990, Discret. Math..

[15] A. Pasini. Gluing two affine spaces. , 1996 .

[16] Barbara Baumeister. Two New Sporadic Semibiplanes Related to M22 , 1994, Eur. J. Comb..