
Title

RWPRI and (2T)_1 flagtransitive linear spaces

Authors

Francis Buekenhout, PaulOlivier Dehaye and Dimitri Leemans

Reference

Beitrage Algebra Geom. 44(2003), nr. 1, 2546.

Abstract

The classification of finite flagtransitive linear spaces is almost complete.
For the thick case, this result was announced by Buekenhout, Delandtsheer, Doyen, Kleidman, Liebeck and Saxl, and in the thin case (where the lines have 2 points), it amounts to the classification of 2transitive groups, which is generally considered to follow from the classification of finite simple groups. These two classifications actually leave an open case, which is the socalled 1dimensional case. In this paper, we work with two additional assumptions. These two conditions, namely (2T)_1 and RWPRI, are taken from another field of study in Incidence Geometry and allow us to obtain a complete classification, which we present at the end of this paper. In particular, for the 1dimensional case, we show that the only (2T)_1 flagtransitive linear spaces are AG(2,2) and AG(2,4), with AGammaL(1,4) and A\GammaL(1,16) as respective automorphism groups.


