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  • Definition: A group is a set G together with a law of composition that has the following properties: a) The law of Composition is associative: (ab)c=a(bc) for all a, b, c in G. b) G contains an identity element 1, such that 1a=a and a1=a for all a in G. c) Every element a of G has an inverse, an element b such that ab=1 and ba=1.

    Source: Algebra, second edition by Michael Artin

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