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On the acylindrical accessibility of finitely presented groups. (Sur l’accessibilité acylindrique des groupes de présentation finie.) (French) Zbl 0999.20017
Summary: Let $$G$$ be a group and $$\tau$$ a $$G$$-tree. In this paper, we assume that $$G$$ does not split as an amalgam $$G=A*_CB$$ or HNN extension $$G=A*_C$$ over a group $$C$$ which stabilizes a segment of length greater than $$k$$ in $$\tau$$ ($$k\geq 2$$); if $$\tau$$ does not contain a proper invariant subtree, we prove that the number of vertices of $$\tau/G$$ is bounded by $$12kT$$, where $$T$$ measures the complexity of a presentation of $$G$$.

##### MSC:
 20E08 Groups acting on trees 20F05 Generators, relations, and presentations of groups 20F65 Geometric group theory 20F67 Hyperbolic groups and nonpositively curved groups 20E06 Free products of groups, free products with amalgamation, Higman-Neumann-Neumann extensions, and generalizations
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