A reduction theorem for primitive binary permutation groups

作者：Wiscons Joshua^*

来源：Bulletin of the London Mathematical Society, 2016, 48(2): 291-299.

DOI：10.1112/blms/bdw005

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) over bar, (y) over bar is an element of X-n, (x) over bar and (y) over bar are G-conjugate if and only if every pair of entries from (x) over bar is G-conjugate to the corresponding pair from (y) over bar. Cherlin has conjectured that the only finite primitive binary permutation groups are S-n, groups of prime order, and affine orthogonal groups V x O(V), where V is a vector space equipped with an anisotropic 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, via the O'Nan-Scott Theorem, to groups with a nonabelian simple socle.

• 出版日期2016-4