Group homomorphism

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Definition

A group homomorphism is a function, [ilmath]f:G\rightarrow H[/ilmath] between two groups, [ilmath](G,\times)[/ilmath] and [ilmath](H,*)[/ilmath] such that:

• [ilmath]\forall a,b\in G[f(a\times b)=f(a)*f(b)][/ilmath]

These are homomorphisms in the categorical sense (of the [ilmath]\mathrm{GROUP} [/ilmath] category)