Andrews–Curtis groups and the Andrews–Curtis conjecture
Adam Piggott · Journal of Group Theory · 2007
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.