In mathematics, given two groups, and, a group homomorphism from to is a function h : G → H such that for all u and v in G it holds that h = h ⋅ h {\displaystyle h=h\cdot h} where the group operation on the left side of the equation is that of G and on the right side that of H. From this property, one can deduce that h maps the identity element eG of G to the identity element eH of H, h = e H {\displaystyle h=e_{H}} and it also maps inverses to inverses in the sense that h = h − 1. Wikipedia