Homological and homotopical finiteness properties of the group E(G)

Abstract

For a group G and an isomorphism of groups ψ: G→ Gψ we study homological and homotopical properties of the group E(G)=⟨G,Gψ∣[D,L]=1⟩,where D= [ G, Gψ] and L= [ G, ψ]. For k≥ 2 we show that E(G) has homotopical type Fk (resp. homological type FPk) if and o