3-cycle or a product of three cycles permutations

[188818881888]

Homework Statement

Show that every element in A(n)= set of even permutations, for n> or equal to 3 can be expressed as a 3-cycle or a product of three cycles.

Homework Equations

3-cycle = (_ _ _). a permutation is a function from a set A to A that is bijective.

The Attempt at a Solution

for n=3 a permuation can be (1 2 3), (1 3 2), (2 1 3), (3 1 2) etc... need help for n>3

 

[Office_Shredder]

What factorization do you already know you can do to an even permutation?

 

[188818881888]

Do you mean how can you express it? You can express an even permutation into a product of even number of 2-cycles. also the order of A(n) is n!/2