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)

Please show steps. Thanks!

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- Apr 24th 2009, 07:56 AMmpryalgroup 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)

Please show steps. Thanks! - Apr 24th 2009, 08:31 AMThePerfectHacker
I do the first one you do the other ones.

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

Thus,

$\displaystyle (123456)(789) = (16)(15)(14)(13)(12)(79)(78)$.

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