[GAP Forum] Computing a subgroup of G which does not map i to j

[Dima Pasechnik]

Dear GAP forum
> 
On Fri, Oct 01, 2004 at 03:30:04PM +0100, Alastair Donaldson wrote:
> I have the following problem:  I have a permutation group G acting on the 
> set 1..n, given by a set of generators.
> 
> I've discovered that one of the generators of G maps a certain value i to 
> a certain value j, and that this is not suitable for my purposes.
> 
> I want a subgroup of G which does not map i to j.  I could throw away all 
> generators that map i to j, but I'd probably lose most of the group then.
the set of elements of G that do not map i to j is not a
subgroup of G.
E.g. the subgroup generated by (ik) and (jk)  - note that
these permutations do not map i to j - 
contains (ij), that does map i to j

The set of elements of G that fixes i and j is a subgrop, that
can be computed using Stabilizer

HTH,
Dmitrii
http://center.uvt.nl/staff/pasechnik/