Constructing coset geometries with Magma : An application to the sporadic groups M(12) and J(1)

Title	Constructing coset geometries with Magma : An application to the sporadic groups M(12) and J(1)
Authors	M. Dehon and D. Leemans
Reference	Atti Sem. Mat. Fis. Univ. Modena L(2002), 415-427.
Abstract	We describe a new algorithm to compute all firm, residually connected geometries on which a given group G acts flag-transitively and residually weakly primitively. We apply this algorithm to classify all geometries with Borel subgroup different from the identity for the Mathieu group M(12). It turns out of this classification that the RWPRI rank of M(12) is equal to 5. Another application allows to identify a geometry missing in [H. Gottschalk and D. Leemans, The Residually Weakly Primitive Geometries of the Janko group J_1, in Groups and Geometries (eds. L. di Martino et al.), Birkhauser, Basel (1998), 65-79] for the Janko group J_1. The complete list of geometries obtained for the Mathieu group M(12) is available as a supplement to this paper. Download a PostScript or a DVI version of the supplement. Download the RWPRI and (2T)_1 geometries of M(12) as a gzipped tarred magma file.