# Permutation confusion

• Oct 7th 2009, 09:08 AM
slevvio
Permutation confusion
any enlightenment about this would be great:) I dont know whether the permutation moves A to where B is in the first picture or if we apply the function to A it becomes C.

http://i712.photobucket.com/albums/w...vvio/group.jpg
• Oct 7th 2009, 10:31 AM
tonio
Quote:

Originally Posted by slevvio
any enlightenment about this would be great:) I dont know whether the permutation moves A to where B is in the first picture or if we apply the function to A it becomes C.

http://i712.photobucket.com/albums/w...vvio/group.jpg

Is the one from the left: why do you think it could be the right one, anyway??

Tonio
• Oct 7th 2009, 10:49 AM
slevvio
because A goes to where B is in the original triangle, B goes to where C is and C goes to where A is

also this is meant to be an example of one of the rotations in the dihedral group for an equilateral triangle
• Oct 7th 2009, 10:53 AM
tonio
Quote:

Originally Posted by slevvio
because A goes to where B is in the original triangle, B goes to where C is and C goes to where A is

Oops! Now that you say that I see both possibilities can happen. I guess it all depends on definitions: are we to understand that the vertices are moved (together with their tag = letter) or else the vertices are kept fixed and we move only the letters??
In the first case the right option is correct, since vertex A is moved to position prviously occupied by vertex B, but in the second case the left one is the correct one.

Tonio
• Oct 7th 2009, 10:55 AM
slevvio
hehe thanks:) also those two are inverses of each other which is interesting hehe. I will find out what convention gets used at this university but thanks for the help:)
• Oct 7th 2009, 11:00 AM
Matt Westwood
It's not something to get hung up on - the group $S_3 = D_3$ or whatever it gets called is generally used only for training purposes, as are the diagrams that illustrate the permutations. So whichever convention is being used, you'll be off them quicker than training wheels on your first pushbike.