|Date||Nov 22, 2016|
Right-angled Artin groups are the graph product whose vertex groups are infinite cyclic groups, which are defined by finite simple graphs.
A finite simple graph is called thin-chordal if it has no induced subgraphs that are isomorphic to either the cycle with 4 vertices or the path with 4 vertices.
We will discuss group properties related to right-angled Artin groups from thin-chordal graphs.
We show that a right-angled Artin group is defined by a thin-chordal graph if and only if every finite index subgroup of the group is a right-angled Artin group.