Submission date: 2 october 2017

Abstract:

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.