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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

An atlas of regular thin geometries
for small groups


Author: Dimitri Leemans
Journal: Math. Comp. 68 (1999), 1631-1647
MSC (1991): Primary 51E24, 52B10, 20B99
Published electronically: May 17, 1999
MathSciNet review: 1654025
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Abstract | References | Similar Articles | Additional Information

Abstract: For some small groups, we give, up to isomorphism, an exhaustive list of all residually connected thin geometries on which these groups act regularly. We then show the utility of such an atlas by proving several results about smallest groups acting on a given diagram. The results have been obtained using a series of MAGMA programs.


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Additional Information

Dimitri Leemans
Affiliation: Université Libre de Bruxelles, Département de Mathématique, C.P.216- Géométrie, Boulevard du Triomphe, B-1050 Bruxelles
Email: dleemans@ulb.ac.be

DOI: http://dx.doi.org/10.1090/S0025-5718-99-01130-8
PII: S 0025-5718(99)01130-8
Keywords: Incidence geometry, group theory, regular maps, polytopes
Received by editor(s): February 10, 1998
Published electronically: May 17, 1999
Additional Notes: This research was accomplished during a stay at the University of Sydney. We gratefully acknowledge support from the Fonds National de la Recherche Scientifique de Belgique and The University of Sydney.
Article copyright: © Copyright 1999 American Mathematical Society