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

[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?

Thanks in advance

 

[CompuChip]

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,

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

Are you sure you meant "not equal"?

 

[Artusartos]

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"?

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