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Toward the recognition of PGLn via a high degree of generic transitivity

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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… Click to show full abstract

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 nā€‰+ā€‰2 where n is the Morley rank of X. Moreover, they conjectured that the bound is only achieved (assuming transitivity) by acting naturally on projective n-space. We solve the problem under the two additional hypotheses that (1) (X, G) is 2-transitive, and (2) has a definable quotient equivalent to . The latter hypothesis drives the construction of the underlying projective geometry and is at the heart of an inductive approach to the main problem.

Keywords: generic transitivity; toward recognition; recognition pgln; pgln via; transitivity; degree generic

Journal Title: Communications in Algebra
Year Published: 2018

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