Every permutation of a finite set can be written as a cycle or as a product of disjoint cycles

Every permutation in $S_n \forall n \geq$ 2 can be written as a product of transposition.

Suppose we have $\alpha=(123)(111)$

As a product of transposition, do I ignore the 'repeating' elements?

So that we have $(12)(13)(11)\equiv (12)(13)$?

  • 2
    $\begingroup$ The notation $(1\ 1\ 1)$ does not define a permutation, so you don't need to bother with that. $\endgroup$ – Arnaud D. Mar 24 '16 at 11:45
  • $\begingroup$ $(123)$ is a permutation but (1,1,1) is??..nothing actually $\endgroup$ – Upstart Mar 24 '16 at 11:46

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