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Dear GAP-Forum,

I have written some time ago an example of an "iterator"-function

which I use in my programs.

Since these functions may be useful for other GAP-users too, I have

put them into a file named 'IRTransversal.g', added some documentation

and copied this file to ftp.math.rwth-aachen.de, directory

pub/incoming.

Here is the documentation part of this file: ## ## This file contains GAP-functions for looping through a list of right ## coset representatives for a permutation group modulo some subgroup ## (which may be trivial), but without producing such a list. ## ## The two functions to use are called 'IterativeRightTransversal' and ## 'NextIRT'. ## ## Let g be a permutation group in GAP and u a subgroup of g. The output ## of 'IterativeRightTransversal(g,u)' is a record <IRT> which mainly ## contains the stabilizer chain of the bigger group. The call of ## 'NextIRT(<IRT>)' produces a new coset representative as long as the ## record component <IRT>.more equals 'true'. ## ## The easiest way to understand the usage may be to look at an example: ## ## ## gap> g:=Group((1,2,3,4),(1,2)); ## Group( (1,2,3,4), (1,2) ) ## gap> u:=Subgroup(g,[(1,2),(3,4)]); ## Subgroup( Group( (1,2,3,4), (1,2) ), [ (1,2), (3,4) ] ) ## gap> irt:=IterativeRightTransversal(g,u);; ## gap> while irt.more do Print(NextIRT(irt),"\n"); od; ## () ## (2,4,3) ## (1,4,2,3) ## (2,3,4) ## (1,4) ## (1,2,3,4) ## gap> irt.more; ## false ## gap> NextIRT(irt); # from now always the last element is returned: ## (1,2,3,4) ## gap> ## ## (OK, this is example is not very interesting because in this case ## 'irt' is bigger than the output of 'RightTransversal'.) ##

I'm anxious to know how such constructs will be realized in future

versions of GAP.

Best regards,

Frank Luebeck

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