(adsbygoogle = window.adsbygoogle || []).push({}); prove that U_{m/n_1} (m) , ....... U_{m/n_k} (m) are normal subgroups

In the attached image I have proved that U_{m/n_1} (m) , ....... U_{m/n_k} (m) are normal subgroups

But how do i Prove that U(m) = U_{m/n_1} (m) ....... U_{m/n_k} (m)?

and that their intersection is identity alone.

Help will be appreciated. Thanks

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# Prove that U_{m/n_1} (m) , . U_{m/n_k} (m) are normal subgroups

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