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

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Given two discrete groups [math]\Gamma,\Lambda[/math], prove that the algebras [math]C^*(\Gamma),C^*(\Lambda)[/math] are independent inside [math]C^*(\Gamma\times\Lambda)[/math], and free inside [math]C^*(\Gamma*\Lambda)[/math].