A
one-to-one mapping φ from a
group G onto another group 
that is operation
preserving, i.e.,
φ(ab) = φ(a)φ(b) for all a, b in G.
A
one-to-one mapping φ from a
group G onto another group that is operation
preserving, i.e.,
φ(ab) = φ(a)φ(b) for all a, b in G.