Let $G$ be the group defined by the following presentation. $$G=\left\langle v,w,x,y,z | [v,w],[w,x],[x,y],[y,z],[z,v],vw^{-1}xy^{-1}zv^{-1}wx^{-1}yz^{-1}\right\rangle.$$ Is it true that the subgroup generated by the squares $v^2,w^2,x^2,y^2,z^2$ is the Right-Angled Artin Group defined by a 5-cycle.
2
-
1$\begingroup$ stupid remark (but to help reading): if you perform the change of variable replacing $w,y$ by inverses, the question is the same with the last relator replaced by $(vwxyz)(zyxwv)^{-1}$ (so the whole group has a presentation with a positive presentation: $vw=wv$, etc, $vwxyz=zyxwv$). The question is whether this last relator affects the subgroup generated by squares of generators. $\endgroup$– YCorCommented Nov 3, 2016 at 22:41
-
$\begingroup$ The definition of right-angled Artin groups should be mentioned. $\endgroup$– M. Farrokhi D. G.Commented Nov 6, 2016 at 14:54
Add a comment
|