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# Products of Conjugacy Classes in $SU(2)$

We obtain a complete description of the conjugacy classes $C_1,\dots,C_n$ in $SU(2)$ with the property that $C_1\cdots C_n=SU(2)$. The basic instrument is a characterization of the conjugacy classes $C_1,\dots,C_{n+1}$ in $SU(2)$ with $C_1\cdots C_{n+1}\ni I$, which generalizes a result of \cite{Je-We}.