A note on finiteness properties of graphs of groups

We show that if G is of type \mathcal {F}_n, and G splits as a finite graph of groups, then the vertex groups are of type \mathcal {F}_n if the edge groups are of type \mathcal {F}_n.

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Bibliographic Details
Published in:Proceedings of the American Mathematical Society. Series B Vol. 8; no. 11; pp. 121 - 128
Main Authors: Haglund, Frédéric, Wise, Daniel
Format: Journal Article
Language:English
Published: 23-03-2021
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Description
Summary:We show that if G is of type \mathcal {F}_n, and G splits as a finite graph of groups, then the vertex groups are of type \mathcal {F}_n if the edge groups are of type \mathcal {F}_n.
ISSN:2330-1511
2330-1511
DOI:10.1090/bproc/81