For the transposition (i j)(k), this is what I have in my

1. Jan 30, 2013

Artusartos

For the transposition (i j)(k), this is what I have in my notes:

$(i j)(k) = k$ if k is not equal to i or j
$(i j)(k) = i$ if k is not equal to j
$(i j)(k) = j$ if k = i

My question:

I thought the product of permuations is again a permutation, but here they are just equal to numbers. Can anybody explain why?

2. Jan 30, 2013

CompuChip

Re: Permutations...

Maybe the brackets a bit confusing, and what you(r teacher) actually meant by (i j)(k) is the result of the transposition (i j) applied to the element k?

Also,
Are you sure you meant "not equal"?

3. Jan 30, 2013

Artusartos

Re: Permutations...

Maybe I copied that wrong. Thanks, I think I understand it now. :)