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:
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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.
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