Abstract
We study Artin kernels, i.e. kernels of discrete characters of right-angled Artin groups, and we show that they decompose as graphs of groups in a way that can be explicitly computed from the underlying graph.
When the underlying graph is chordal, we show that every such subgroup either surjects to an infinitely generated free group or is a generalized Baumslag–Solitar group of variable rank.
In particular, for block graphs (e.g. trees), we obtain an explicit rank formula and discuss some features of the space of fibrations of the associated right-angled Artin group.
Abstract
We establish conditions under which the fundamental group of a graph of finite p-groups is necessarily residually p-finite.
The technique of proof is independent of previously established results of this type, and the result is also valid for infinite graphs of groups.
Virtual communities of practice are gaining importance as mean of sharing and exchanging knowledge. In such environments, information reuse is of major concern. In this paper, the authors outline the importance of structuring documents in order to facilitate the reuse of their content. They show how explicit structure representation facilitates the understanding of the original documents and helps considerably in automating the reuse process. The authors propose two main tools: the first performs automatic structure transformation using matching techniques and the second performs structure and instances evolution in a transparent and an automatic manner.
Abstract
We study the quasi-isometric rigidity of a large family of finitely generated groups that split as graphs of groups with virtually free vertex groups and two-ended edge groups.
Let G be a group that is one-ended, hyperbolic relative to virtually abelian subgroups, and has JSJ decomposition over two-ended subgroups containing only virtually free vertex groups that are not quadratically hanging.
Our main result is that any group quasi-isometric to G is abstractly commensurable to G. In particular, our result applies to certain “generic” HNN extensions of a free group over cyclic subgroups.
Accuracy of automatic structure propagation for daily magnetic resonance image-guided head and neck radiotherapy
