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The residually weakly primitive geometries of \(\text{PSL} (3,q)\) with \(q < 8\). (English) Zbl 1052.51003

Summary: We announce the classification of all firm and residually connected geometries satisfying the condition \((2T)_1\) and on which a \(\text{PSL}(3,q)\) group (with \(q<8\)) acts flag-transitively and residually weakly primitively. The complete list of geometries is available as a supplement to this note [cf. the authors, ”Supplement to: The residually weakly primitive geometries of \(\text{PSL}(3,q)\) with \(q<8\)”, available at http://cso.ulb.ac.be/~dleemans/abstracts/psl3.html].

MSC:

51E14 Finite partial geometries (general), nets, partial spreads
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