Normalising graphs of groups

Christian Krattenthaler; Thomas W. Müller

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arXiv · 1608.03538

Normalising graphs of groups

Christian Krattenthaler·Thomas W. Müller

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Abstract

We discuss a partial normalisation of a finite graph of finite groups $(\Gamma(-), X)$ which leaves invariant the fundamental group. In conjunction with an easy graph-theoretic result, this provides a flexible and rather useful tool in the study of finitely generated virtually free groups. Applications discussed here include (i) an important inequality for the number of edges in a Stallings decomposition $\Gamma \cong \pi_1(\Gamma(-), X)$ of a finitely generated virtually free group, (ii) the proof of equivalence of a number of conditions for such a group to be `large', as well as (iii) the classification up to isomorphism of virtually free groups of (free) rank $2$. We also discuss some number-theoretic consequences of the last result.

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BibTeX RIS

Christian Krattenthaler, Thomas W. Müller. 2016-08-11. Normalising graphs of groups. https://arxiv.org/abs/1608.03538

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