Abelian implies universal power map is endomorphism

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Let (G, +) be an Abelian group, and n be an integer. The map g \mapsto ng (i.e., the map g \mapsto g + g + \dots + g done n times when n is positive and (-g) + (-g) + \dots + (-g) done (-n) times when n is negative) is an endomorphism of G.


Given: An Abelian group G, an integer n.

To prove: The map g \mapsto ng is an endomorphism of G: in other words, n(g + h) = ng + nh.

Proof: The proof basically follows from commutativity. PLACEHOLDER FOR INFORMATION TO BE FILLED IN: [SHOW MORE]