Abstract
Let F be the free group on two letters. For ω \in F we study the associated word map ω: SU(n) \times SU(n) \rightarrow SU(n). Extending a method of Goto, we show that for ω not in the second derived subgroup F^(2) of F, there are infinitely many n \in N such that the associated word map ω : SU(n) \times SU(n) \rightarrow SU(n) is surjective.
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