Thread: write (12345) as product of 3 cycles

Hi,

I need help on how to write (12345) as product of 3-cycles. Any suggestion?

Thank you.

Originally Posted by nguy0688

I need help on how to write (12345) as product of 3-cycles.

Do you know how to express (12345) as a product of transpositions? If so, just pair off the transpositions to form 3-cycles.

More specifically, (12345) = (15)(14)(13)(12). The product (15)(14) is a 3-cycle, and so is (13)(12).

Try to show something stronger: every even permutation on n>2 letters is a product of 3-cycles.