University:

Martin-Luther-Universitaet Halle-Wittenberg

Department:

Mathematik und Informatik

Institut fuer Algebra und Geometrie

Date: 21.03.2002

MSC:

20D08 Simple groups: sporadic groups

20E32 Simple groups, See also {20D05}

51E24 Buildings and the geometry of diagrams

Language: written in ENG

Abstract: This thesis considers amalgams for the O'Nan sporadic simple group related to flag-transitive geometries of Buekenhout, resp. of Ivanov and Shpectorov. It is shown that these amalgams are uniquely determined by the residues of rank three, resp. of rank four. Moreover it is shown that the geometry of Buekenhout and the 3-fold cover of the geometry of Ivanov and Shpectorov are simply connected. The proofs for these results involve computer calculations. Without using these results it is proved that every completion of the amalgam of the geometry of Buekenhout has an irreducible 154-dimensional $GF(3)$-module and is also a completion of the amalgam of the geometry by Ivanov and Shpectorov.