Thread: Fun with normal subgroups.

This stuff drives me bonkers. Anyway, I have been given or have proved the following:

is onto.



is a subgroup

is a subgroup of

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My last question (for this section) is:

Verify that if is normal in , then is normal in

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Can I say this:

If is normal in then:

for all , so:





for all

Hence, is normal in

That's perfect. Of course, it all comes down to the fact that can be any element of . You should perhaps write that down explicitly.