The paper by Buekenhout, Delandtsheer, Doyen, Kleidman, Liebeck and Saxl called *Linear spaces with flag transitive automorphism groups* (Geom. Dedicata) from 1990 annonces a very powerful classification result for the objects mentioned in the title. However, it does not contain any proofs.


In a recent paper (Feng 2017) the paper is cited together with another one by Kantor, *2-transitive and flag transitive designs*, but the latter is a survey and does not contain proofs, either.


Surely in 2019 the details must be available somewhere! And I keep seeing the Buekenhout paper mentioned in different places, so the confidence in the result seems high.



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> What is a good reference, with proofs, for this classification result?
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Thanks!



About the paper by Buekenhout, Delandtsheer, Doyen, Kleidman, Liebeck and Saxl
The proof for this appeared over a series of papers. The final one was


Jan Saxl, `[On Finite Linear Spaces with Almost Simple Flag-Transitive Automorphism Groups](http://dx.doi.org/10.1006/jcta.2002.3305)' Journal of Combinatorial Theory, Series A 100, 322–348 (2002).


which includes references for all the papers.


