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Invariants and examples of group actions on trees and length functions

Published online by Cambridge University Press:  20 January 2009

David L. Wilkens
David L. Wilkens
Affiliation:
School of Mathematics and StatisticsUniversity of BirminghamBirminghamB15 2TTEngland
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An action of a group G on a tree, and an associated Lyndon length function l, give rise to a hyperbolic length function L and a normal subgroup K having bounded action. The Theorem in Section 1 shows that for two Lyndon length functions l, l′ to arise from the same action of G on some tree, L = L′ and K = K′. Moreover for L non-abelian L = L′ implies K = K′. That this is not so for abelian L is shown in Section 2 where two examples of Lyndon length functions l, l′ on an H.N.N. group are given, with their associated actions on trees, for which L = L′ is abelian but K≠K′.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 34 , Issue 2 , June 1991 , pp. 313 - 320
Copyright
Copyright © Edinburgh Mathematical Society 1991

References

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