The residually weakly primitive geometries of \(M_{22}\)
The author announces the classification of all firm and residually connected geometries satisfying the conditions \((IP)_2\) and \((2T)_1\) on which the Mathieu group \(M_{22}\) acts flag-transitively and residually weakly primitively. This is achieved by using MAGMA programs described by \textit{M. Dehon} and the author [Constructing coset geometries with MAGMA: An application to the sporadic groups \(M_{12}\) and \(J_1\). Atti Sem. Mat. Fis. Univ. Modena 50, 415-427 (2002)]. The author obtained no geometries of rank at least 6 and 7, 25, 16 and 9 geometries of rank 2, 3, 4 and 5, respectively. The full list of geometries, giving their diagrams, automorphism and correlation groups, Borel subgroups and kernels, can be obtained as a supplement to the paper at\break http://cso.ulb.ac.be/\(\sim\)dleemans/abstracts/m22.html. Also the full subgroup pattern of \(M_{22}\) is given there.
scientific article; zbMATH DE number 1968866