Given two groups G , G ′ {\displaystyle G,G'} , a homomorphism from G {\displaystyle G} to G ′ {\displaystyle G'} is a function ϕ : G → G ′ {\displaystyle \phi :G\to G'\,} such that for all a , b ∈ G {\displaystyle a,b\in G} , ϕ ( a b ) = ϕ ( a ) ϕ ( b ) {\displaystyle \phi (ab)=\phi (a)\phi (b)\,}
