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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.

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

Thanks!

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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' Journal of Combinatorial Theory, Series A 100, 322–348 (2002).

which includes references for all the papers.

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