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All automorphisms of free groups with maximal rank fixed subgroups

Published online by Cambridge University Press:  24 October 2008

D. J. Collins  and
E. C. Turner
D. J. Collins
Affiliation:
School of Mathematical Sciences, Queen Mary and Westfield College, Mile End Road, London E1 4NS
E. C. Turner
Affiliation:
Department of Mathematics, University at Albany, Albany, NY 12222
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Extract

The Scott Conjecture, proven by Bestvina and Handel [2] says that an automorphism of a free group of rank n has fixed subgroup of rank at most n. We characterise in Theorem A below those automorphisms that realise this maximum. It follows from this characterisation, for example, that any such automorphism has linear growth. In our paper [3], we generalised the Scott Conjecture to arbitrary free products, using Kuros rank (see Section 2 below) in place of free rank; in Theorem B, we characterise those automorphisms of a free product realising the maximum. We show that in this case the growth rate is also linear. These results extend those of [4].

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 119 , Issue 4 , May 1996 , pp. 615 - 630
Copyright
Copyright © Cambridge Philosophical Society 1996

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References

REFERENCES

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