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Maximal hyperbolic towers and weight in the theory of free groups

Part of: Structure and classification of infinite or finite groups Special aspects of infinite or finite groups Model theory

Published online by Cambridge University Press:  18 November 2019

BENJAMIN BRÜCK
BENJAMIN BRÜCK*
Affiliation:
Fakultät für Mathematik, Universität Bielefeld, Postfach 100131, D-33501 Bielefeld, Germany. e-mail: benjamin.brueck@uni-bielefeld.de
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Abstract

We show that in general for a given group the structure of a maximal hyperbolic tower over a free group is not canonical: we construct examples of groups having hyperbolic tower structures over free subgroups which have arbitrarily large ratios between their ranks. These groups have the same first order theory as non-abelian free groups and we use them to study the weight of types in this theory.

MSC classification

Primary: 20F65: Geometric group theory
Secondary: 03C45: Classification theory, stability and related concepts 20E05: Free nonabelian groups
Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 170 , Issue 3 , May 2021 , pp. 479 - 498
Copyright
© Cambridge Philosophical Society 2019

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