The polynomial automorphisms of some certain groups

Let A(G) denote the automorphism group of a group G. A polynomial automorphism of G is an automorphism of the form X→(v^1_-1 x^ ϵ1V_1)…(V^-1_m x^ ϵmV_m). We shall write P(G)=(P)(G)) such that P_0(G) is the set of polynomial automorphisms of G. In this paper, we will prove that P_0(D8) ∼= V_4 and P(Q) = A(Q), where Q is the additive group.