# Graph products of groups

@inproceedings{Green1990GraphPO, title={Graph products of groups}, author={Eli R. Green}, year={1990} }

In the 1970's Baudisch introduced the idea of the semifree group, that is, a group in which the only relators are commutators of generators. Baudisch was mainly concerned with subgroup problems, employing length arguments
on the elements of these groups. More recently Droms and Servatius have continued the study of semifree, or graph groups, as they call them. They answer some of the questions left open by the work of Baudisch. It is
possible to take the graph analogy a level higher and study…

## 211 Citations

### Centralizers in graph products of semigroups

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The first author of this article together with Gould studied the closure properties of graph products of monoids with respect to abundancy and Fountanicity (which may be viewed as weaker forms of…

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### Generalising some results about right-angled Artin groups to graph products of groups

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### Limit groups over partially commutative groups and group actions on real cubings

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The study of limit groups, that is, finitely generated fully residually free groups, was a key first step towards the understanding of the elementary theory of a free group. In this paper we conduct…

### Conjugacy growth series of groups

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In this thesis we study the conjugacy growth series of several group constructions in terms of the standard and the conjugacy growth series of the building groups, with a specific generating set.…

### Automorphisms of graph products of groups and acylindrical hyperbolicity.

- Mathematics
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This article is dedicated to the study of the acylindrical hyperbolicity of automorphism groups of graph products of groups. Our main result is that, if $\Gamma$ is a finite graph which contains at…

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In this work we use geometric techniques in order to study certain natural extensions of free groups, and solve several algorithmic problems on them.
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### Automorphisms of graph products of groups from a geometric perspective

- MathematicsProceedings of the London Mathematical Society
- 2019

This article studies automorphism groups of graph products of arbitrary groups. We completely characterise automorphisms that preserve the set of conjugacy classes of vertex groups as those…

### On Subgroups of the Pentagon Group

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Given a graph Γ with vertex set X, the graph group of Γ, denoted by G(Γ), is the group generated by the elements of X subject to the relations xy = yx for each pair x and y of adjacent vertices in Γ.…

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