Some stably tame polynomial automorphisms

We study the structure of length three polynomial automorphisms of R[X,Y]R[X,Y] when RR is a UFD. These results are used to prove that if SLm(R[X1,X2,…,Xn])=Em(R[X1,X2,…,Xn])SLm(R[X1,X2,…,Xn])=Em(R[X1,X2,…,Xn]) for all n≥0n≥0 and for all m≥3m≥3 then all length three polynomial automorphisms of R[X,Y]R[X,Y] are stably tame.