Coinitial Grapfis and Whitehead Automorphisms

Source abstract

Coinitial graphs were used in [ 2 ; 3 ; 4 ] as a combinatorial tool in the Reidemeister- Schreier process in order to prove subgroup theorems for Fuchsian groups. Whitehead had previously introduced such graphs but used topological methods for his proofs [ 8 ; 9 ]. Subsequently Rapaport [ 7 ] and Iliggins and Lyndon [ 1 ] gave algebraic proofs of the results in [ 9 ], and AIcCool [ 5 ; 6 ] has further developed these methods so that presentations of automorphism groups could be found. In this paper it is shown that Whitehead automorphisms can be described by a “cutting and pasting” operation on coinitial graphs. Section 1 defines and gives some combinatorial properties of these operations, based on [ 1 ].