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.