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arXiv · 1812.04866

Two-ended quasi-transitive graphs

Babak Miraftab·Tim Rühmann
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Abstract

The well-known characterization of two-ended groups says that every two-ended group can be split over finite subgroups which means it is isomorphic to either by a free product with amalgamation $A\ast_C B$ or an HNN-extension $\ast_ϕ C$, where $C$ is a finite group and $[A:C]=[B:C]=2$ and $ϕ\in Aut(C)$. In this paper, we show that there is a way in order to spilt two-ended quasi-transitive graphs without dominated ends and two-ended transitive graphs over finite subgraphs in the above sense. As an application of it, we characterize all groups acting with finitely many orbits almost freely on those graphs.

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Babak Miraftab, Tim Rühmann. 2018-12-12. Two-ended quasi-transitive graphs. https://arxiv.org/abs/1812.04866

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