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order g

order g

ExampleOrder and StructureCounting by Order of Elementsin Relation to HomomorphismsClass EquationReferencesThe symmetric group S3 has the following multiplication table. This group has six elements, so ord(S3) = 6. By definition, the order of the identity, e, is one, since e 1 = e. Each of s, t, and w squares to e, so these group elements have order two: |s| = |t| = |w| = 2. Finally, u and v have order 3, since u3 = vu = e, and v3 = uv = e.See more on en.wikipedia.orgEstimated Reading Time: 6 minsORDERS OF ELEMENTS IN A GROUP Introduction kconrad.math.uconn.edu/blurbs/grouptheory/order.pdfPDF fileORDERS OF ELEMENTS IN A GROUP 3 When gn = e, nmight not be as small as possible, so the repetition in the powers of g may really occur more often than every nturns. For example, ( 1)4 = 1, so Theorem3.1 says the only powers of 1 are ( 1)k for k2f0;1;2;3g, but we know that in

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