If (G,·) is a group, let (M(G), +, o) be the set of all mappings from G to G, with pointwise addition and with the composition of mappings as multiplication: if g ∈ G and α,β ∈ G and α,β ∈ M(G), by definition g(α + β) = (gα)·(gβ) and g(52L?o β) = (gα)β. Then (M(G), +, o) is a near-ring.
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