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10 - Generalized Baumslag-Solitar groups: a topological approach
Edited by C. M. Campbell, University of St Andrews, Scotland, M. R. Quick, University of St Andrews, Scotland, E. F. Robertson, University of St Andrews, Scotland, C. M. Roney-Dougal, University of St Andrews, Scotland, D. I. Stewart, University of Manchester
Book:

Groups St Andrews 2022 in Newcastle

Published online:

21 November 2024

Print publication:

12 December 2024, pp 407-440
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Summary

Generalized Baumslag-Solitar groups are a class of combinatorially interesting groups. Their group theory is also closely associated to a the topology of a class of 2-dimensional spaces. These 2-dimensional spaces are Seifert fibred. We develop the basic topology of these fibrations and derive some of the most immediate group theoretic consequences of this topology.

Cyclic orders and graphs of groups
Part of
- Structure and classification of infinite or finite groups
- Special aspects of infinite or finite groups
Harrison J. McDonough, Daniel T. Wise
Journal:

Proceedings of the Edinburgh Mathematical Society , First View

Published online by Cambridge University Press:

21 October 2024, pp. 1-12
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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.

5 - What is a hierarchically hyperbolic space?
from Part Two - Expository Articles
Edited by Mark Hagen, University of Bristol, Richard Webb, University of Cambridge, Henry Wilton, University of Cambridge
Book:

Beyond Hyperbolicity

Published online:

22 June 2019

Print publication:

11 July 2019, pp 117-148
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Summary

The first part of this survey is a heuristic, non-technical discussion of what an HHS is, and the aim is to provide a good mental picture both to those actively doing research on HHSs and to those who only seek a basic understanding out of pure curiosity. It can be read independently of the second part, which is a detailed technical discussion of the axioms and the main tools to deal with HHSs.

On Certain Finitely Generated Subgroups of Groups Which Split
Myoungho Moon
Journal:

Canadian Mathematical Bulletin / Volume 46 / Issue 1 / 01 March 2003

Published online by Cambridge University Press:

20 November 2018, pp. 122-129

Print publication:

01 March 2003
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Define a group $G$ to be in the class $S$ if for any finitely generated subgroup $K$ of $G$ having the property that there is a positive integer $n$ such that ${{g}^{n\,}}\in \,K$ for all $g\,\in \,G,\,K$ has finite index in $G$. We show that a free product with amalgamation $A{{*}_{_{C}}}B$ and an $\text{HNN}$ group $A{{*}_{C}}$ belong to $S$, if $C$ is in $S$ and every subgroup of $C$ is finitely generated.

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