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We show that the only transitive and generically 4-transitive action of a group of finite Morley rank on a set of Morley rank 2 is the natural action of PGL on the projective plane.
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Tuna Altınel, Joshua Wiscons, Recognizing PGL via generic 4-transitivity. J. Eur. Math. Soc. 20 (2018), no. 6, pp. 1525–1559DOI 10.4171/JEMS/792