Consider the alternating group A4. Identify the groups N and A4 /N up to an isomorphism.

Thank you very much. Can you write the Caley table of each of the subgroups of each non-abelian group of order 8

Please do Part ACE and please show step by step and explain

Find an example of a noncyclic group, all of whose proper subgroupsare cyclic.

Find all the generators of the following cyclic groups: (Z/6Z,+), ((Z/5Z)*, ·), (2Z, +), ((Z/11Z)*, ·).

If G is a group under the binary operation (*), Then (a*b)-1=(b-1)*(a-1). Proof this statement with additional explanation, thank you in advance.

Let G = Zp × Zp. Is this group cyclic? As you know any cyclic group canbe generated by one element. If G is not cyclic how many elements you need to generate this group. What is the smallest size of a generating set?