The paper by Buekenhout, Delandtsheer, Doyen, Kleidman, Libeck 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!

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!