Journal of the European Mathematical Society

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Volume 20, Issue 6, 2018, pp. 1525–1559
DOI: 10.4171/JEMS/792

Published online: 2018-05-07

Recognizing PGL$_3$ via generic 4-transitivity

Tuna Altınel[1] and Joshua Wiscons

(1) Université Claude Bernard Lyon 1, France

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$_3$ on the projective plane.

Keywords: Primitive permutation groups, multiple transitivity, finite Morley rank

Altınel Tuna, Wiscons Joshua: Recognizing PGL$_3$ via generic 4-transitivity. J. Eur. Math. Soc. 20 (2018), 1525-1559. doi: 10.4171/JEMS/792