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Some Remarks on IA Automorphisms of Free Groups

Published online by Cambridge University Press:  20 November 2018

J. McCool
J. McCool*
Affiliation:
University of Toronto, Toronto, Ontario
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Let An be the automorphism group of the free group Fn of rank n, and let Kn be the normal subgroup of An consisting of those elements which induce the identity automorphism in the commutator quotient group . The group Kn has been called the group of IA automorphisms of Fn (see e.g. [1]). It was shown by Magnus [7] using earlier work of Nielsen [11] that Kn is finitely generated, with generating set the automorphisms

and

where x1, x2, …, xn, is a chosen basis of Fn.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 40 , Issue 5 , 01 October 1988 , pp. 1144 - 1155
Copyright
Copyright © Canadian Mathematical Society 1988

References

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