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**aliceinwonderland** -----------------------------------------------------------------

(1) An endomorphism f of a group G is called normal endomorphism if $\displaystyle af(b)a^{-1} = f(aba^{-1})$ for all $\displaystyle a,b \in G$.

(2) f + g denotes the function G->G given by $\displaystyle a \mapsto f(a)g(a) $.

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[Hungerford, p88, Q3.8]

Let f and g be normal endomorphisms of a group G. Prove that if f + g is an endomorphism, then it is normal.