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 <[email protected]> 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 <[email protected]>
> Sent: 23 April 2021 08:27
> To: [email protected]
> 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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