Given two groups G , G â² {\displaystyle G,G'} , a homomorphism from G {\displaystyle G} to G â² {\displaystyle G'} is a function Ï : G â G â² {\displaystyle \phi :G\to G'\,} such that for all a , b â G {\displaystyle a,b\in G} , Ï ( a b ) = Ï ( a ) Ï ( b ) {\displaystyle \phi (ab)=\phi (a)\phi (b)\,}
