Andrews-Curtis groups and the Andrews-Curtis conjecture

For an integer n at least two and a positive integer m, let C(n,m) denote the group of Andrews-Curtis transformations of rank (n,m) and let F denote the free group of rank n + m. A subgroup AC(n,m) of Aut(F) is defined, and an anti-isomorphism AC(n,m) to C(n,m) is described. We solve the generalized word problem for AC(n,m) in Aut(F) and discuss an associated reformulation of the Andrews-Curtis conjecture.