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Let G {\displaystyle G} and H {\displaystyle H} be groups. A semihomomorphism from G {\displaystyle G} to H {\displaystyle H} is a map f : G → H {\displaystyle f:G\to H} that satisfies, for all a , b ∈ G {\displaystyle a,b\in G} :
f ( a b a ) = f ( a ) f ( b ) f ( a ) {\displaystyle f(aba)=f(a)f(b)f(a)}
