[math] \newcommand{\mathds}{\mathbb}[/math]

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Consider a discrete group generated by elements of finite order, written as a quotient group, as follows:

[[math]] \mathbb Z_{N_1}*\ldots*\mathbb Z_{N_k}\to\Gamma [[/math]]

Prove that we have an embedding [math]\widehat{\Gamma}\subset S_N^+[/math], where [math]N=N_1+\ldots+N_k[/math].