Assignment:
See the following cayley tables:
Determine the order of each element x ∈ G. Prove that G is a cyclic group.
• Let S3 be the symmetric group of degree 3 together with composition of maps. Is G isomorphic to S3? Justify your answer.
• Let p be a prime number and G a group of order p2 with identity element e. let U ≠ G and U ≠ {e} be a subgroup of G. prove that U is cyclic.
Provide complete and step by step solution for the question and show calculations and use formulas.