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Preprint Number 1312

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1312. Tuna Altinel and Joshua Wiscons
Towards the recognition of PGL_n via a high degree of generic transitivity

Submission date: 2 october 2017


In 2008, Borovik and Cherlin posed the problem of showing that the degree of generic transitivity of an infinite permutation group of finite Morley rank (X,G) is at most n+2 where n is the Morley rank of X. Moreover, they conjectured that the bound is only achieved (assuming transitivity) by PGL_{n+1}(F) acting naturally on projective n-space. We solve the problem under the two additional hypotheses that (1) (X,G) is 2-transitive, and (2) (X-{x},G_x) has a definable quotient equivalent to (P^{n-1}(F),PGL_{n}(F)). The latter hypothesis drives the construction of the underlying projective geometry and is at the heart of an inductive approach to the main problem.

Mathematics Subject Classification: 20B22, 03C60

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Full text arXiv 1710.00445: pdf, ps.

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