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Final remark: the above comments subsume all comments and answers to mathoverflow.32351.

Final remark: the above comments subsume all comments and answers to mathoverflow.32351.

I am trying to determine whether the literature contains a complete proof of the classification of finite 2-transitive groups. This is a fundamental result with important applications in many areas of mathematics, so it seems worthwhile to make sure that it has actually been proved. In short, the issue is that it is common to credit Hering for classifying the nonsolvable affine 2-transitive groups, but it seems that Hering never published a paper containing such a classification; and the one paper which does purport to contain a proof, namely a 1985 paper by Liebeck, begins with a logical leap which I cannot follow.

I am trying to determine whether the literature contains a complete proof of the classification of finite 2-transitive groups. This is a fundamental result with important applications in many areas of mathematics, so it seems worthwhile to make sure that it has actually been proved. In short, the issue is that it is common to credit Hering for classifying the nonsolvable affine 2-transitive groups, but it seems that Hering never published a paper containing such a classification; and the one paper which does purport to contain a proof, namely a 1985 paper by Liebeck, begins with a logical leap which I cannot follow. [Added later: thanks to Michael Giudici's answer, I can now follow the first step in Liebeck's proof. I have not yet gone through the rest of the proof, but do not presently have any reason to doubt its validity.]

Maillet 1895: Sur les isomorphes holédriques et transitifs des groupes symériques ou alternés, J. Math. Pure. Appl. 1 (1895), 5-34.

Huppert 1957: Zweifach transitive, auflosbare Permutations Gruppen, Math. Z. 68 (1957), 126-150.

Hering 1974: Transitive groups and linear groups which contain irreducible subgroups of prime order, Geom. De. 2 (1974), 425-460.

Curtis-Kantor-Seitz 1976: The 2-transitive permutation representations of the finite Chevalley groups, Trans. Amer. Math. Soc. 218 (1976), 1-59. (For corrigenda, see the paper's Math.Review.)

Maillet 1895: Sur les isomorphes holoédriques et transitifs des groupes symétriques ou alternés, J. Math. Pures Appl. (5) 1 (1895), 5-34.

Huppert 1957: Zweifach transitive, auflösbare Permutationsgruppen, Math. Z. 68 (1957), 126-150.

Hering 1974: Transitive groups and linear groups which contain irreducible subgroups of prime order, Geometriae Dedicata 2 (1974), 425-460.

Curtis-Kantor-Seitz 1976: The 2-transitive permutation representations of the finite Chevalley groups, Trans. Amer. Math. Soc. 218 (1976), 1-59. (For corrigenda, see the paper's Math.Review.)