Fundamental groups of graphs of groups satisfy the finitely generated intersection property precisely when vertex groups, edge double cosets, and graph structure meet stated conditions, with an explicit decidable criterion for graphs of locally quasi-convex hyperbolic groups with virtually Z edge 2.
Discrete Groups of Motions
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The finitely generated intersection property in fundamental groups of graphs of groups
Fundamental groups of graphs of groups satisfy the finitely generated intersection property precisely when vertex groups, edge double cosets, and graph structure meet stated conditions, with an explicit decidable criterion for graphs of locally quasi-convex hyperbolic groups with virtually Z edge 2.