# Can the infinite von Dyck groups be subgroups of $SU(n)$?

I know by constructing some particular cases that I can find unitary matrices $X$, $Y$ and $Z$ such that

$X^m = Y^n = Z^p = XYZ = 1$

with

$$\frac{1}{m} + \frac{1}{n}+\frac{1}{p} < 1$$

indicating an infinite von Dyck group unless the fact that the matrices are unitary implies some additional, non-trivial relations between $X$, $Y$ and $Z$. Is it possible for infinite von Dyck or triangle groups to be subgroups of $SU(n)$?

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What have you tried? –  draks ... Jul 23 '12 at 8:00