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.
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