question 1) Prove that .
question 2) Prove that if with , then for all subgroups K of G either or,
.
I dont know how to solve the first one but i could solve the second one.
here is my solution of the second one:
since we find that so .
also and so it makes sense to consider .
Using we get,
.
This means either
this easily lads to the desired result.
If you have a different solution to the second one then please post it.