Some stably tame polynomial automorphisms

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