1. prove no two of C_8, C_4 X C_2, C_2 X C_2 X C_2 are isomorphic.C_n is cyclic group of order n.

Give, with justification, a group of order 8 that is not isomorphic to any of those groups.

2. Prove that if m and n are coprime then C_m X C_n is cyclic.

if m and n are not coprime. can it be cyclic?

3. H is a normal subgroup of a finite group G. Which of the followings are true?

(i) if G is cyclic then H and G/H are cyclic.

(ii) If H and G/H are cyclic then G is cyclic.

(iii) If G is abelian then H and G/H are abelian

(iv) If H and G/H are abelian then G is abelian.

4. find all homomorphisms between C_11 to C_14

5. H is a subgroup of G and H not equal to G. Show that there is an element of G which does not belong to any subgroup of the form gHg^(-1) for g belongs to G