Exercise
Consider the product of the cycles (2,3,4)(1,3,4)(1,2,4)(1,2,3). Which of the following is its disjoint cycles decomposition?
The identity
(2,3,4)(1,3,4)(1,2,4)(1,2,3)
(1,2,3,4)
(1,2)(3,4)
That is right. It is equal to the identity, the empty product.
No, the supports of the cycles have to be disjoint.
Wrong, this permutation differs from the given one.
Wrong, this permutation differs from the given one.