RWPRI and \((2T)_1\) flag-transitive linear spaces
The classification of all pairs \((\Gamma,G)\), where \(G\) is a group acting flag-transitive and faithfully on a finite linear space \(\Gamma\) is almost complete. For the thick case, the result was announced in [\textit{F. Buekenhout, A. Delandtsheer, J. Doyen, P. Kleidman, M. Liebeck} and \textit{J. Saxl}, Geom. Dedicata 36, 89-94 (1990; Zbl 0707.51017)]. In the thin case, it amounts to the classification of 2-transitive groups, which is generally considered to follow from the classification of finite simple groups. The so-called 1-dimensional case is still open in the two classifications. In the present paper, the authors obtain a complete classification (including the 1-dimensional case) if \(\Gamma\) is \text{RWPri} (residually weakly primitive) or \((2T)_1\) (\(G\) is 2-transitive on all rank 1 residues of \(\Gamma\)).
scientific article; zbMATH DE number 1894841