Amalgamation and the invariant trace field of a Kleinian group

Abstract

Let Γ be a Kleinian group of finite covolume and denote by Γ (2) the subgroup generated by {γ 2 :γ ∈ Γ}. In [9] the trace field of Γ (2) was shown to be an invariant of the commensurability class of Γ. In [8] this field was termed the invariant trace field of Γ and further properties of this field were studied. Following the notation of [8] we denote the invariant trace field of Γ by k (Γ).