Homework Help: Let a and b belong to Sn. Prove that (a^-1)(b^-1)(a)(b) is an even permutation.

1. Feb 14, 2008

tyrannical608

1. The problem statement, all variables and given/known data
Let a and b belong to Sn. Prove that (a^-1)(b^-1)(a)(b) is an even permutation.

2. Relevant equations
Definitions I have are
Every permutation in Sn, n>1 is a product of 2 cycles
and
A permutation that can be expressed as a product of an even number of 2 cycles is called an even permutation

Thanks

2. Feb 14, 2008

HallsofIvy

So, it appears you are saying that all the permutations involved in $a^{-1}b^{-1}ab$ is a two-cycle and this is a product of 4 of them!

3. Feb 16, 2008

tyrannical608

Maybe its my flu...but what do you mean exactly? What I said are two definitions out of the book.

Do I have to show that a^-1b^-1 is one cycle and that ab is another cycle?

4. Feb 16, 2008

AKG

If a can be expressed as a product of k 2-cycles, what can you say about how many 2-cycles it takes to express a-1?