Submission date: 12 June 2015.

Abstract:

A permutation group (X,G) is said to be binary, or of relational complexity 2, if for all n, the orbits of G (acting diagonally) on X^2 determine the orbits of G on X^n in the following sense: for all x,y in X^n, x and y are G-conjugate if and only if every pair of entries from x is G-conjugate to the corresponding pair from y. Cherlin conjectured that the only finite primitive binary permutation groups are S_n, groups of prime order acting regularly, and affine orthogonal groups V ⋊ O(V) where V is a vector space equipped with an anistropic quadratic form. Recently he succeeded in establishing the conjecture for those groups with an abelian socle. In this note we show that what remains of the conjecture reduces to groups with a nonabelian simple socle.

Mathematics Subject Classification: Primary 20B15, Secondary 03C13

Keywords and phrases:

Full text arXiv 1506.04187: pdf, ps.