On coherence of graph products of groups and Coxeter groups

2019 ◽  
Vol 342 (7) ◽  
pp. 2100-2105 ◽  
Author(s):  
Olga Varghese
Keyword(s):  
Coxeter Groups ◽  
Graph Products ◽  
Products Of Groups

scholarly journals SURFACE SUBGROUPS OF GRAPH PRODUCTS OF GROUPS

2012 ◽  
Vol 22 (08) ◽  
pp. 1240003
Author(s):  
SANG-HYUN KIM
Keyword(s):  
Direct Product ◽  
Finite Groups ◽  
Coxeter Groups ◽  
Surface Group ◽  
Hyperbolic Surface ◽  
Graph Products ◽  
Graph Product ◽  
Cyclic Groups ◽  
Products Of Groups ◽  
Product Kernel

Let G be a graph product of a collection of groups and H be the direct product of the same collection of groups, so that there is a natural surjection p : G → H. The kernel of this map p is called a graph product kernel. We prove that a graph product kernel of countable groups is special, and a graph product of finite or cyclic groups is virtually cocompact special in the sense of Haglund and Wise. The proof of this yields conditions for a graph over which the graph product of arbitrary nontrivial groups (or some cyclic groups, or some finite groups) contains a hyperbolic surface group. In particular, the graph product of arbitrary nontrivial groups over a cycle of length at least five, or over its opposite graph, contains a hyperbolic surface group. For the case when the defining graphs have at most seven vertices, we completely characterize right-angled Coxeter groups with hyperbolic surface subgroups.

Graph products of groups and group spaces

1995 ◽  
Vol 53 (1-2) ◽  
pp. 131-147 ◽  
Author(s):  
Jochen Pfalzgraf
Keyword(s):  
Graph Products ◽  
Products Of Groups

scholarly journals The Identity Problem for Graph Products of Groups

1993 ◽  
Vol 162 (1) ◽  
pp. 168-177 ◽  
Author(s):  
Y.G. Baik ◽  
J. Howie ◽  
S.J. Pride
Keyword(s):  
Graph Products ◽  
Identity Problem ◽  
Products Of Groups

ORDERING GRAPH PRODUCTS OF GROUPS

2012 ◽  
Vol 22 (04) ◽  
pp. 1250037 ◽  
Author(s):  
I. M. CHISWELL
Keyword(s):  
Graph Products ◽  
Graph Product ◽  
Free Products ◽  
Products Of Groups

It is shown that a graph product of right-orderable groups is right orderable, and that a graph product of (two-sided) orderable groups is orderable. The latter result makes use of a new way of ordering free products of groups.

scholarly journals Automorphisms of graph products of groups from a geometric perspective

2019 ◽  
Vol 119 (6) ◽  
pp. 1745-1779 ◽  
Author(s):  
Anthony Genevois ◽  
Alexandre Martin
Keyword(s):  
Graph Products ◽  
Products Of Groups

scholarly journals Bredon cohomological dimension for virtually abelian stabilisers for CAT(0) groups

2019 ◽  
pp. 1-13 ◽  
Author(s):  
Tomasz Prytuła
Keyword(s):  
Finite Groups ◽  
Discrete Group ◽  
Coxeter Groups ◽  
Cohomological Dimension ◽  
Fundamental Groups ◽  
Graph Products ◽  
The Family ◽  
Abelian Subgroups ◽  
Right Angled Artin Groups ◽  
Cube Complexes

Given a discrete group [Formula: see text], for any integer [Formula: see text] we consider the family of all virtually abelian subgroups of [Formula: see text] of rank at most [Formula: see text]. We give an upper bound for the Bredon cohomological dimension of [Formula: see text] for this family for a certain class of groups acting on CAT(0) spaces. This covers the case of Coxeter groups, Right-angled Artin groups, fundamental groups of special cube complexes and graph products of finite groups. Our construction partially answers a question of Lafont.

On graph products of multipliers and the Haagerup property for -dynamical systems

2019 ◽  
Vol 40 (12) ◽  
pp. 3188-3216
Author(s):  
SCOTT ATKINSON
Keyword(s):  
Dynamical Systems ◽  
Positive Definite ◽  
Alternative Proof ◽  
Discrete Groups ◽  
Graph Products ◽  
Graph Product ◽  
Haagerup Property ◽  
Products Of Groups ◽  
Product Action

We consider the notion of the graph product of actions of discrete groups $\{G_{v}\}$ on a $C^{\ast }$-algebra ${\mathcal{A}}$ and show that under suitable commutativity conditions the graph product action $\star _{\unicode[STIX]{x1D6E4}}\unicode[STIX]{x1D6FC}_{v}:\star _{\unicode[STIX]{x1D6E4}}G_{v}\curvearrowright {\mathcal{A}}$ has the Haagerup property if each action $\unicode[STIX]{x1D6FC}_{v}:G_{v}\curvearrowright {\mathcal{A}}$ possesses the Haagerup property. This generalizes the known results on graph products of groups with the Haagerup property. To accomplish this, we introduce the graph product of multipliers associated to the actions and show that the graph product of positive-definite multipliers is positive definite. These results have impacts on left-transformation groupoids and give an alternative proof of a known result for coarse embeddability. We also record a cohomological characterization of the Haagerup property for group actions.

Sign in / Sign up

Export Citation Format

Share Document