An isomorphism is a bijective homomorphism \(f:G\to H\) of two algebraic structures \((G,\ast)\), \((H,\cdot)\)
\[f(a\ast b)=f(a)\cdot f(b).\]
If an isomorphism exists between \((G,\ast)\), \((H,\cdot),\) we write \(G\simeq H\) and say that \(G\) and \(H\) are isomorphic.
Proofs: 3 4 5
Theorems: 6 7 8 9