[GAP Forum] All factorizations of a permutation

[Ahmet Arıkan]

Hi Chris, thank you for the reply. 

My main problem is to construct a group G in Sym(\Omega) satisfying the following property: 

G has a generating subset X such that every infinite subset of X also generates G.

 So to construct such a group, we may start with an element x (say x=(1,3,4) ) to contruct X. Then we need to find suitable factorizations like (1,3,4)=(1,2,3,4)*(2,3) ( or multiple factorizations)  and  continue to construct X={(1,3,4), (1,2,3,4),(2,3),...}. This is just an explanation of why I want to find suitable factorizations of permutations.

We do not know yet if such a perfect locally finite (p-) group G exists.

Best wishes,

Ahmet

Christopher Jefferson <caj21 at st-andrews.ac.uk> şunları yazdı (23 Nis 2021 10:44):

> Hi Ahmet,
> 
> You might have to make your problem a little clearer.
> 
> Do you just want factorisations of a permutation into two parts, p*q?
> 
> Then, for any permutation p, p*(p^-1*(1,3,4)) = (1,3,4), so for any p you can calculate q=p^-1*(1,3,4).
> 
> Chris
> 
> -----Original Message-----
> From: Ahmet Arıkan <arikan at gazi.edu.tr> 
> Sent: 23 April 2021 08:27
> To: forum at gap-system.org
> Subject: [GAP Forum] All factorizations of a permutation
> 
> Dear Forum,
> 
> I am almost new in GAP
> Is it possible to find all factorizations by GAP of a permutation in arbitrary S_n for suitable n. For example (1,3,4)=(1,2,3,4)*(2,3). How about all factorizations of (1,3,4) in S_5.
> 
> Thanks in advance,
> 
> Ahmet Arikan
> 
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