Cherlin's conjecture for almost simple groups of Lie rank 1

GILL NICK; HUNT FRANCIS; SPIGA PABLO

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Cherlin's conjecture for almost simple groups of Lie rank 1

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Abstract A permutation group G on a set Ω is said to be binary if, for every n ∈ ℕ and for every I, J ∈ Ωn, the n-tuples I and J are in the same G-orbit if and only if every pair of entries from I is in the same G-orbit to the corresponding pair from J. This notion arises from the investigation of the relational complexity of finite homogeneous structures.Cherlin has conjectured that the only finite primitive binary permutation groups are the symmetric groups Sym(n) with their natural action, the groups of prime order, and the affine groups V ⋊ O(V) where V is a vector space endowed with an anisotropic quadratic form.We prove Cherlin's conjecture, concerning binary primitive permutation groups, for those groups with socle isomorphic to PSL2(q), 2B2(q), 2G2(q) or PSU3(q). Our method uses the notion of a “strongly non-binary action”.

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《Mathematical Proceedings of the Cambridge Philosophical Society》 |2019年第3期|417-435|共19页
作者
GILL NICK; HUNT FRANCIS; SPIGA PABLO;
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University of South Wales;

University of Milano-Bicocca;

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正文语种英语
中图分类数学;
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Cherlin's conjecture for almost simple groups of Lie rank 1

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