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

[vish_maths]

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

 

[Greg Bernhardt]

I'm sorry you are not generating any responses at the moment. Is there any additional information you can share with us? Any new findings?

 

[disregardthat]

What is U(m)?