TSSFL TECHNOLOGY STACK

Isomorphism is a map between two groups, which is a bijection (one-to-one and onto) such that $f:G \rightarrow G'$. E.g., $f(x,y) = f(x)f(y)$ gives isomorphism.

In other words, an isomorphism $f:G \rightarrow G'$ is a homomorphism that is one-to-one and onto. $G$ is isomorphic to $G'$ is denoted by $G \simeq G'$.

Fact: Every two cyclic groups of order $n$ are isomorphic (Prove).

If the group is cyclic it means there is an element in it that generates the entire group.

Homomorphism and Isomorphism