[GAP Forum] Product of Subgroups in a Group

[Benjamin Sambale]

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.Reichard at 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.murthy at 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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