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Coinitial Grapfis and Whitehead Automorphisms

Published online by Cambridge University Press:  20 November 2018

A. H. M. Hoare
A. H. M. Hoare*
Affiliation:
University of Birmingham, Birmingham, England
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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].

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 31 , Issue 1 , 01 February 1979 , pp. 112 - 123
Copyright
Copyright © Canadian Mathematical Society 1979

References

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