Published 23 Dec 2004. First received 02 Apr 2004.

An algorithmic analysis of the intersection property

Pascale Jacobs and Dimitri Leemans

Abstract: In this paper, efficient algorithms are given to test the intersection property and some of its variations on flag-transitive coset geometries. These algorithms are then applied to geometries of some sporadic groups, namely the Mathieu groups M₁₁, M₁₂, M₂₂ and M₂₃, the Janko groups J₁, J₂ and J₃, and the Higman–Sims group HS.

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In addition to the paper, the following electronic appendices are available to subscribers :

Appendix A : This appendix contains the source code given in Section 6 of the paper, provided as a text file. The file can be loaded in MAGMA using the `load' command.

Appendix B : This appendix comprises a gzipped tar archive of text files that contain the maximal parabolic subgroups of the geometries for the eight smallest sporadic groups mentioned in the paper. The archive also contains a README file, explaining how to use the files in MAGMA.

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