A Classification of Flag-transitive Classical c.C2-geometries by Means of Generators and Relations

A readable and uniform proof of the classification of the flag-transitive classical c.C2-geometries with s ? 3 is provided, by means of generators and relations. As by-products, explicit presentations of U5(2), McL and a triple cover of U4(3) are obtained.

[1]  Mark A. Ronan,et al.  Minimal Parabolic Geometries for the Sporadic Groups , 1984, Eur. J. Comb..

[2]  J. J. Seidel,et al.  The regular two-graph on 276 vertices , 1975, Discret. Math..

[3]  Mark A. Ronan,et al.  Finite Geometries and Designs: Coverings of certain finite geometries , 1981 .

[4]  Satoshi Yoshiara,et al.  Embeddings of flag-transitive classical locally polar geometries of rank 3 , 1992 .

[5]  ArjehM. Cohen,et al.  Affine polar spaces , 1989 .

[6]  Jacques Tits.  Non-existence de certaines extensions transitives: I. Groupes projectifs à une dimension , 1971 .

[7]  Alexandre A. Ivanov,et al.  On 2-Transitive Graphs of Girth 5 , 1987, Eur. J. Comb..

[8]  Antonio Pasini,et al.  Extended generalized quadrangles , 1990 .

[9]  A. Neumaier,et al.  Distance Regular Graphs , 1989 .

[10]  A. Pasini,et al.  Flag-transitive extensions ofCn geometries , 1991 .

[11]  Jacques Tits,et al.  Ensembles ordonnés, immeubles et sommes amalgamées , 1986 .

[12]  Francis Buekenhout,et al.  Locally polar spaces and related rank 3 groups , 1977 .

[13]  Mark Ronan,et al.  Lectures on Buildings , 1989 .

[14]  Satoshi Yoshiara,et al.  A lattice theoretical construction of a GAB of the Suzuki sporadic simple group , 1988 .

[15]  Hans Cuypers.  Finite locally generalized quadrangles with affine planes , 1992, Eur. J. Comb..

[16]  Gernot Stroth.  Some geometry for MCL , 1989 .

[17]  Satoshi Yoshiara,et al.  A geometric characterization of the groups Suz and HS , 1990 .

[18]  Gary M. Seitz.  Flag-Transitive Subgroups of Chevalley Groups , 1973 .

[19]  Richard Weiss.  A geometric characterization of the groups McL and Co3 , 1991 .

[20]  B. Fischer,et al.  Finite groups generated by 3-transpositions. I , 1971 .

[21]  William M. Kantor,et al.  Generalized polygons, SCABs and GABs , 1986 .

[22]  Antonio Pasini.  On locally polar geometries whose planes are affine , 1990 .

[23]  Michio Suzuki.  Transitive extensions of a class of doubly transitive groups , 1966 .