Take the 2-minute tour ×
MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.

When working with group cosets in MAGMA is there a way of treating the cosets as subsets of the overlying group. Specifically I have a group $G$ and subgroups $H$ and $K$ . I wish to look at the intersection of a pair of cosets $Hh$ and $Kk$ for some $h,k\in G$ , but am unable to perform such operations in MAGMA when they are considered as cosets.

share|improve this question
add comment

2 Answers

up vote 2 down vote accepted

As far as I can see, the only way to do that directly with cosets $ C1$ and $C2$ of $G$ is

$\{ x : x\ {\rm in}\ G\ |\ x\ {\rm in}\ C1\ {\rm and}\ x\ {\rm in}\ C2 \}$

which looks very inefficient, because it is iterating over all of $G$.

I would suggest first find a right transversal $T$ of $H \cap K$ in $H$, and then search through $T$ looking for an element $t \in T$ with $thk^{-1} \in K$. If you find such a $t$, then the intersection is the coset $(H \cap K)th$, and otherwise it is empty.

share|improve this answer
    
Thanks for that. I was using a similar kind of approach and looping through the cosets of the two groups. –  dward1996 Apr 3 '12 at 8:45
add comment

Well, this is trivial in GAP. Here is an example:

gap> G:=SymmetricGroup(7);; 
gap> H:=Stabilizer(G,1);;
gap> K:=SylowSubgroup(G,2);;
gap> c1:=RightCoset(H,(1,2));;  
gap> c2:=RightCoset(K,(1,2,3));;
gap> Intersection(c1,c2);      
[ (1,2,3), (1,2,3)(5,6), (1,2,3,4), (1,2,3,4)(5,6) ]
gap> 

By the way, GAP is free, unlike Magma...

share|improve this answer
1  
Thanks. I was trying to avoid using GAP for now, as I'm only just getting the hang of MAGMA, but it appears that it is worth investing the time to learn the language. –  dward1996 Apr 3 '12 at 8:45
    
IMHO, GAP language is easier to use, in particular it's much less strict in the ways it handles types of data. And you can read (and modify, if needed) the GAP source code if you're really stuck :-) –  Dima Pasechnik Apr 3 '12 at 17:06
    
Just out of interest are there any other good sources for learning GAP other than the GAP manuals (gap-system.org/Doc/manuals.html)? –  dward1996 Apr 4 '12 at 8:38
    
gap-system.org/Doc/Learning/learning.html contains quite a few links to tutorials, examples, etc. gap-system.org/Doc/forumarchive.html (GAP Forum) is a mailing list you can subscribe to. –  Dima Pasechnik Apr 4 '12 at 14:09
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.