MATH 3175 Study Guide - Final Guide: Cayley Table, Centralizer And Normalizer, Symmetric Group
9 Jan 2019
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Final exam: let g be the group de ned by the following cayley table. 8 (a) for each element a g, nd: the order |a|; the inverse a 1; and the centralizer c(a). Fall 2010: let = (cid:20)1 2 3 4 5 6 7. 4 7 5 1 3 6 2(cid:21), viewed as elements in the symmetric group s7. (a) compute the products (b) compute the inverses. 1 = (c) compute the conjugate of by : 1 = (d) do and commute: let = (cid:20)1 2 3 4 5 6 7 8 9. Fall 2010: let r be the additive group of real numbers, and let r be the multiplicative group of non-zero real numbers. In each case, explain why. (a) u (15) and z8. (b) a4 and d12. (c) s4 and d6 z2. Fall 2010: let s3 be the group of permutations of the set {1, 2, 3}.
