Group homomorphism

Common card · No. 377086

In mathematics, given two groups, (G,∗) and (H, ·), a group homomorphism from (G,∗) to (H, ·) is a function h : G → H such that for all u and v in G it holds that h ( u ∗ v ) = h ( u ) ⋅ h ( v ) {\displaystyle h(u*v)=h(u)\cdot h(v)} 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 G ) = e H {\displaystyle h(e_{G})=e_{H}} and it also maps inverses to inverses in the sense that h ( u...

Read on Wikipedia · Image Cronholm144, CC BY-SA 3.0