Group Theory : Cayley Tables, Cyclic Groups and Isomorphisms
? I have the following cayley tables (which is in modulo 9)
determine the order of each element . Prove that G is a cyclic group.
? Let be the symmetric group of degree 3 together with composition of maps. Is G isomorphic to ? Justify your answer.
? Let p be a prime number and G a group of order with identity element e. let and be a subgroup of G. prove that U is cyclic.