See also the thread "complex product of two groups" in the forum archive:
http://mail.gap-system.org/pipermail/forum/2012/thread.html#3628 Cheers, William On Fri, Feb 15, 2013 at 10:51 AM, Benjamin Sambale <benjamin.samb...@gmail.com> wrote: > See also SetX(H,K,PROD) > > Benjamin > > Am 15.02.2013 15:47, schrieb Sandeep Murthy: > >> the duplicates can be removed using >> >> Unique( ListX( H, K, PROD ) ). >> >> Seems fairly quick, but maybe for large products >> DoubleCoset (H, One(H), K), suggested by Burkhard, >> is quicker. >> >> Sincerely, Sandeep. >> >> Burkhard Höfling wrote: >>> >>> On 2013-02-15, at 10:35 , Sven Reichard<sven.reich...@tu-dresden.de> >>> wrote: >>> >>>> -----BEGIN PGP SIGNED MESSAGE----- >>>> Hash: SHA1 >>>> >>>> Am 15.02.2013 10:02, schrieb rahul kitture: >>>>> >>>>> Given two subgroups $H$ and $K$ of a finite group (say Symmetric/ >>>>> Alternating Group), how do we compute the product $HK$ in the >>>>> group? I couldn't find anything from Help or topics in online >>>>> library. >>>> >>>> This may not be the most elegant way, but >>>> gap> Group(Concatenation(List([H,K], GeneratorsOfGroup)), Identity(H)); >>>> should do the trick. >>> >>> >>> >>> This gives the subgroup generated by H and K but not, in general, the set >>> HK. If you know that HK is a subgroup, then this will work. ClosureGroup >>> (H,K) might be a bit more efficient. >>> >>> On 2013-02-15, at 14:27 , Sandeep Murthy<sandeepr.mur...@gmail.com> >>> wrote: >>> >>>> Hi, >>>> >>>> If H, K are subgroups of G then >>>> >>>> ListX( H, K, PROD ) >>>> >>>> will return a (mutable) list of >>>> the elements >>>> of the set HK in >>>> G. >>> >>> >>> But note that the list will have duplicates if H and K don't intersect >>> trivially. >>> >>> I would suggest DoubleCoset (H, One(H), K) to represent HK more >>> efficiently. You can turn the double coset into a list via AsList/ >>> AsSSortedList. >>> >>> Cheers >>> >>> Burkhard. >>> >>> _______________________________________________ >>> Forum mailing list >>> Forum@mail.gap-system.org >>> http://mail.gap-system.org/mailman/listinfo/forum >> >> >> _______________________________________________ >> Forum mailing list >> Forum@mail.gap-system.org >> http://mail.gap-system.org/mailman/listinfo/forum >> > > > _______________________________________________ > Forum mailing list > Forum@mail.gap-system.org > http://mail.gap-system.org/mailman/listinfo/forum _______________________________________________ Forum mailing list Forum@mail.gap-system.org http://mail.gap-system.org/mailman/listinfo/forum
