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group homomorphism

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
${\\displaystyle h(u*v)=h(u)\\cdot h(v)}$
where the group operation on the left side of the equation is that of G and on the right side that of H.
(Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Group_homomorphism)

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