Subgroups of IA automorphisms of a free group

ORIN CHEINwhich take every generator of F into a conjugate of itself will be studied.It will be shown that this group is just C (the subgroup generated by the double indexed generators of K), and a set of defining relations for this group will be found.In section 6, a theorem about T (the group generated by the triple indexed generators of K) being free will be stated, with some discussion of the proof.And finally, in section 7, some comments about some known relations in K will be made, leading to some conjectures about the structure of K.I would like to express my appreciation to Wilhelm Magnus for the invaluable advice, help, and encouragement he provided to me during my research for this paper. NotationWe will use a = al, b = a2, and c = a 3 to denote a set of free generators of F = F 3.If/~ is an automorphism given by alz=O~, bp=fl, cp=~, then p will frequently be denoted by ~u: (a; b; c) -~ (~; fl; ~) or in some contexts just by (~;/~; ~). 9 If p, ~ E A = .43,then p~ means first apply ~ to (a; b; c) and then