Altınel, Tuna Recognizing \(\mathrm{PGL}_3\) via generic 4-transitivity. (English) Zbl 1494.20005 J. Eur. Math. Soc. (JEMS) 20, No. 6, 1525-1559 (2018). Summary: 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 \(\mathrm{PGL}_3\) on the projective plane. Cited in 4 Documents MSC: 20B22 Multiply transitive infinite groups 03C60 Model-theoretic algebra 20F11 Groups of finite Morley rank 20G40 Linear algebraic groups over finite fields Keywords:primitive permutation groups; multiple transitivity; finite Morley rank PDFBibTeX XMLCite \textit{T. Altınel}, J. Eur. Math. Soc. (JEMS) 20, No. 6, 1525--1559 (2018; Zbl 1494.20005) Full Text: DOI arXiv