# group permutations 1

• April 24th 2009, 08:56 AM
mpryal
group permutations 1
Find the parity of each permutation:

b) (1 2 3 4 5 6)(7 8 9)
c) (1 2 3 4 5 6)(1 2 3 4 5 7)
d) (1 2)(1 2 3)(4 5)(5 6 8)(1 7 9)

• April 24th 2009, 09:31 AM
ThePerfectHacker
Quote:

Originally Posted by mpryal
Find the parity of each permutation:

b) (1 2 3 4 5 6)(7 8 9)
c) (1 2 3 4 5 6)(1 2 3 4 5 7)
d) (1 2)(1 2 3)(4 5)(5 6 8)(1 7 9)

I do the first one you do the other ones.

Notice, $(123456) = (16)(15)(14)(13)(12)$ and $(789)=(79)(78)$.
Thus,
$(123456)(789) = (16)(15)(14)(13)(12)(79)(78)$.

Notice there are $7$ transpositions, so it is an odd permutation.