Say in $S_4$, I want to write $(1,2,3,4)$ as a product of 3 cycles? How should I do it? In general, how do you decompose larger cycles as the product of smaller cycles (but all having the same cycle length)?
Decomposing larger cycles as the product of smaller cycles
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abstract-algebra
group-theory
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1Well, your permutation is odd, and 3-cycles are even, so you cannot do it: any product of even permutations is even. – 2011-03-23