[GAP Forum] Blocks and block systems for non-transitive groups
wh at icparc.ic.ac.uk
wh at icparc.ic.ac.uk
Wed Dec 1 20:55:18 GMT 2004
Dear Beth, Dear GAP Forum,
On Wed, Dec 01, 2004 at 03:53:25PM +0000, Petra Holmes wrote:
> You can look at each orbit of G on the points separately. To do this, you
> can use the code:
>
> o:=Orbits(G); ims:=[];
> for oo in o do
> hom:=ActionHomomorphism(G,oo,OnPoints);
> Add(ims,Image(hom));
> od;
>
> Then you can look at blocks in each orbit of G separately, as you are now
> dealing with a collection of transitive groups.
Thank you. That would indeed allow me to find all the blocks I wanted
within each orbit using standard routines.
Having given some more thought to the problem, however, I am particularly
interested in blocks than span more than one orbit for intransitive groups.
To give an example, the group generated by (1,2,3,4)(5,6,7,8) is
intransitive: it has two orbits. Considering the orbits independently one
obtains the representative blocks [1,3] and [5,7]. But there are also block
systems with representative blocks [1,3,5,7] and [1,5] that I would like to
find but cannot by considering the orbits independently. Perhaps they can
be recovered/extracted later? But unless that's straightforward to do it
seems as though one might as well use a block-finding algorithm that works
directly with intransitive groups (unless that turns out to be unexpectedly
hard).
I guess I should go study the source code for AllBlocks some more and see if
I can figure out how it works. :)
Cheers,
Warwick
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