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Actions of locally nilpotent groups on Λ-trees

Published online by Cambridge University Press:  14 November 2011

I. M. Chiswell
I. M. Chiswell
Affiliation:
School of Mathematical Sciences Queen Mary and Westfield College, University of London Mile End Road. London E1 4NS, UK
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Abstract

For certain classes of groups, it is shown that there are restrictions on the type of action a group in the class can have on a Λ-tree, where Λ is an arbitrary ordered abelian group, generalizing results by other authors in the case Λ = ℝ. The main classes considered are locally nilpotent, polycyclic by finite, locally (polycyclic by finite) and locally (hyperabelian by finite). The arguments involve an investigation of the relation between the type of action a group has on a Λ-tree and the type of action of its subgroups by restriction.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 129 , Issue 5 , 1999 , pp. 913 - 924
Copyright
Copyright © Royal Society of Edinburgh 1999

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