Hi, I have the following problem related to programming in GAP, hoping someone could help please.
Let G be a permutation group. Let P be the subgroup of G consisting of all "perfect" permutations in G. The goal is to find P explicitly. For this it's enough to check only the (double)coset representatives, since if P is a subgroup of perfect permutations found so far and g (in G) is not perfect, then so is every element in PgP. So part of my codes is as follow: #--------------------------------------------------------------------------------------------------- P:=Subgroup(G,[]); #set P = trivial first D:=DoubleCosetRepsAndSizes(G, P, P); # create list of double coset representatives to be checked i:=2; # skip checking the identity D[1][1] While i <= Size(D) and Size(P) < Size(G) do x:=D[i][1]; if (x is perfect) then P:=ClosureSubgroup(G,x); # add x in the subgroup P D:=DoubleCosetRepsAndSizes(G, P, P); #create new representatives to be tested i:=2; #skip checking the identity; else i:=i+1; fi; od; #--------------------------------------------------------------------------------------------------- The group P will grow over time so the list D will be smaller and smaller. If we are lucky we don't even need to run over all elements in D because P could be G. But the problem is that, the permutation group G is usually very large so the command D:=DoubleCosetRepsAndSizes(G, P, P); takes a very long time (sometime even returns error due to not enough memory). I think it's because the program is trying to build the whole list D first before running over each element. But I just want the program to start right away without building the whole list first. For example it can choose a random first element then at the end of the loop find the next (random) representative and so on. In Magma there is the command TransversalProcess(G, H) http://magma.maths.usyd.edu.au/magma/handbook/text/571 that will do just that . I was wondering if there is a similar command in GAP? (I also tried the build-in command SubgroupByProperty. This gave me the answer almost instantly, but when trying to list all elements, it took a very long time.) Thank you for your time, Pornrat _______________________________________________ Forum mailing list Forum@mail.gap-system.org http://mail.gap-system.org/mailman/listinfo/forum
