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Necessary and sufficient conditions for simplicity of a general skew group ring A?(sigma)G are not known. In this article, we show that a skew group ring A?(sigma)G, of an abelian group G, is simple if and only if its centre is a field and A is G-simple. As an application, we show that a transformation group (X, G), where X is a compact Hausdorff space acted upon by an abelian group G, is minimal
