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Unformatted text preview: (i) Prove that if and are (not necessarily disjoint) permutations that commute, then () k = k k for all k 1. Solution. We prove f rst, by induction on k 1, that k = k . The base step is true because and commute. For the inductive step, k + 1 = k = k ( inductive hypothesis ) = k = k + 1 . We now prove the result by induction on k 1. The base step is obviously true. For the inductive step, () k + 1 = () k = k k ( inductive hypothesis ) = k k ( proof above ) = k + 1 k + 1 ....
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This note was uploaded on 12/21/2011 for the course MAS 4301 taught by Professor Keithcornell during the Fall '11 term at UNF.
 Fall '11
 KeithCornell

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