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Why are the permutations (1 4 2 6)(2 3 4 5) and (1 4 5 6)(2 3) equal? It seems to me as if the first pair of 4-cycles want to permute 4->2 and 4->5, yielding a contradiction, but I suspect I've misunderstood something about composite cycles.

I suspect it has something to do with dividing the cycles into [tex]\alpha[/tex] = (1 4 2 6) and [tex]\beta[/tex] = (2 3 4 5) and investigating the composite function [tex]\alpha \beta[/tex] (or [tex]\beta \alpha[/tex]?), but I can't seem to get the result right.

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# Homework Help: Cycle notation for permutations?

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