2-closures of primitive permutation groups of holomorph type

Abstract

The 2-closure G(2) of a permutation group G on a finite set Ω is the largest subgroup of Sym(Ω) which has the same orbits as G in the induced action on Ω × Ω. In this paper, the 2-closures of certain primitive permutation groups of holomorph simple and holomorph compound types are determined.

Keywords

• 2-closure
• primitive permutation group
• holomorph type
• 05c25
• 20b15
• 20b30