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- W2040960421 abstract "A tree action (G, X), consisting of a group G acting on a tree X, is encoded by a ‘quotient graph of groups’ A=G⧹⧹X. We introduce here the appropriate notion of morphism A→A′= G′⧹⧹X′, that encodes a morphism (G, X)→(G′, X′) of tree actions. In particular, we characterize ‘coverings’ G⧹⧹X→G′⧹⧹X corresponding to inclusions of subgroups G⩽G′. This is a useful tool for producing subgroups of G with prescribed properties. It also yields a strong Conjugacy Theorem for groups acting freely on X. We also prove the following mild generalizations of theorems of Howie and Greenberg. Suppose that G acts discretely on X, i.e. that each vertex stabilizer is finite. Let H and K be finitely generated subgroups of G. Then H∩K is finitely generated. If H and K are commensurable, then H (and K) have finite index in 〈H, K〉." @default.
- W2040960421 created "2016-06-24" @default.
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- W2040960421 date "1993-10-01" @default.
- W2040960421 modified "2023-10-10" @default.
- W2040960421 title "Covering theory for graphs of groups" @default.
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- W2040960421 doi "https://doi.org/10.1016/0022-4049(93)90085-8" @default.
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