The $(p,q,r)$ triangle group is the group with presentation $[a,b | a^p=b^q=(ab)^r=1]$. Has anyone classified the (infinite) quotients of the $(2,4,4)$ triangle group?
$\begingroup$
$\endgroup$
3
-
8$\begingroup$ The triangle group in question has a normal subgroup of index 8 isomorphic to $\mathbb{Z}^2$. Therefore, any quotient has a normal subgroup of index at most 8 that's a quotient of $\mathbb{Z}^2$. How much more information do you need? $\endgroup$– HJRWMar 4, 2011 at 3:55
-
1$\begingroup$ So, in other words, yes. $\endgroup$– Pete L. ClarkMar 4, 2011 at 10:06
-
1$\begingroup$ That subgroup of index 8 is the commutator, so every quotient has a commutator which is (i) of index at most 8 and (ii) a quotient of $\mathbb{Z}^2$. $\endgroup$– Steve DMar 4, 2011 at 16:51
Add a comment
|