Subgroups of IA automorphisms of a free group

Generators and defining relations for the group A n of automorphisms of a free group of rank n were derived by J . Nielsen [11]. For n = 2, this is a fairly easy task, but for n ~> 3 it requires very difficult combinatorial arguments which have not been simplified since the appearance of Nielsen's paper. In order to obtain an easier approach to the investigation of An and a bet ter understanding of its structure, it seems natural to s tudy its subgroups. For all n, the elements of An which induce the identical automorphism in the commutator quotient group Fn/F'~ form a normal subgroup K of An. Bachmuth [1] calls this the group of IA automorphisms of F n. Magnus [8] showed tha t this subgroup is generated by the automorphisms Ktj : ai ~ a ja i a i 1