Let Cn be a cyclic group of order n.

A. How many sub-groups of order 4 there are in C2xC4... explain.

Put , then it's easy to check that the following are sbgps. of order 4 of : , Try now to mimick the above with the group below.
B. How many sub-groups of order p there are in CpxCpxC(p^2) when p is a prime? explain.

C. Prove that if H is cyclic of order 8 then Aut(H) is a non-cyclic group. WHAT is its order?

If , then any is completely and uniquely determined by , and since this must be an AUTOMORPHISM it follows that has to be a generator of the group, so , with . Now check that this can't be a cyclic group, say by finding two different elements (i.e., automorphisms) of order 2...
D. What is the Automorphism group of an infinite cyclic group?

Just as above: the image of a generator MUST be a generator, so....what are the generators of and what're the possibilities of homomorphisms between them...
About A-> it's obvious (because it has index 2) that a subgroup of order 4 is normal...

Oh, dear: much easier! EVERY sbgp. of an abelian group is trivially normal... Tonio
But I can't figure out how many subgroups of this form there are...

About the other parts-I've no idea...

I'll be delighted to get guidance about all the parts in this question.

Tnx in advance...