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Cyclic orders and graphs of groups

Part of: Structure and classification of infinite or finite groups Special aspects of infinite or finite groups

Published online by Cambridge University Press:  21 October 2024

Harrison J. McDonough  and
Daniel T. Wise
Harrison J. McDonough
Affiliation:
Department of Mathematics and Statistics, McGill University, Montreal, QC, Canada
Daniel T. Wise*
Affiliation:
Department of Mathematics and Statistics, McGill University, Montreal, QC, Canada
*
Corresponding author: Daniel T. Wise, email: [email protected]
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Abstract

We examine a cyclic order on the directed edges of a tree whose vertices have cyclically ordered links. We use it to show that a graph of groups with left-cyclically ordered vertex groups and convex left-ordered edge groups is left-cyclically orderable.

Keywords

cyclic orderinggraph of groups

MSC classification

Primary: 20F60: Ordered groups 20E06: Free products, free products with amalgamation, Higman-Neumann-Neumann extensions, and generalizations
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 67 , Issue 4 , November 2024 , pp. 1125 - 1136
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Copyright
© The Author(s), 2024. Published by Cambridge University Press on Behalf of The Edinburgh Mathematical Society.

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