> On 13 Feb 2016, at 20:24, Peter Cameron <p...@mcs.st-andrews.ac.uk> wrote:
>
> Dear GAP forum,
>
> It seems that GAP can find representatives for all systems of minimal blocks
> of imprimitivity for an arbitrary group action, but all blocks only for a
> permutation group (and there seems no easy way to get all maximal blocks).
>
You can build up from minimal blocks recursively, of course. Take the action on
the blocks of a minimal block
system and find the minimal blocks there, they correspond to non-minimal block
systems for the original action, etc.
> I have tried to get around this as follows. G is a group acting on O (which
> is actually an orbit on 2-subsets of [1..n]). I do the following:
>
> GG:=Action(G,O,OnSets);
> BB:=AllBlocks(GG);
> B:=List(BB,x->List(x,y->O[y]));
>
> This assumes that the Action maps each element of O to its position in the
> list, and I can't find a guarantee to this effect in the manual. Can I rely
> on this?
I believe so, although this is (at least) a documentation failing). The manual
does say:
40.3-2 Action homomorphisms
See ActionHomomorphism (41.7-1).
The calculation of images is determined by the acting function used and -for
large domains- is often dominated by the search for the position of an
image in a list of the domain elements. This can be improved by sorting this
list if an efficient method for \< (31.11-1) to compare elements of the
domain is available.
which strongly suggests to me that it is retaining the given order for the
domain.
Steve
>
> Thanks for any advice.
>
> Peter Cameron.
>
>
>
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