Automorphism Groups of the Imprimitive Complex Reflection Groups II

Abstract

We prove that the automorphism group Aut (m,p,n) of an imprimitive complex reflection group G(m,p,n) is the product of a normal subgroup T(m,p,n) by a subgroup R(m,p,n), where R(m,p,n) is the group of automorphisms that preserve reflections and T(m,p,n) consists of automorphisms that map every element of G(m,p,n) to a scalar multiple of itself.