[GAP Forum] changing right- to left multiplication

[Alexander Hulpke]

Dear Forum, Dear David Romano,

>
> I'm very new to GAP, and am for now primarily interested in using  
> GAP as a pedagogical tool for teaching group theory (and possibly   
> ring theory).
>
> At the moment, what I would like to be able to do is have students  
> use standard cycle notation for permutation groups, but have  
> multiplication reflect composition of transformations being read  
> right to left.  Is there any way to do this?

No. Alas most textbooks in the US introduce permutation groups acting  
from the left (which most research-level texts in group theory act  
from the right.
When we designed GAP we decided on action from the right and this is  
implicitly built into much of the code. Short of recoding the whole  
system it would be impossible to redefine the permutation  
multiplication and have the system work consistently.

Considering the use for teaching, I found that students had little  
problems with the fact that the computer multiplied the permutations  
the other way round (though Gallian's 5th edition still makes a  
mistake with it ...)

(You also might find some useful related material on an old course  
homepafge of mine:
http://www.math.colostate.edu/~hulpke/lectures/m366/index.html)

Best wishes,

     Alexander Hulpke


-- Colorado State University, Department of Mathematics,
Weber Building, 1874 Campus Delivery, Fort Collins, CO 80523-1874, USA
email: hulpke at math.colostate.edu, Phone: ++1-970-4914288
http://www.math.colostate.edu/~hulpke