[GAP Forum] Find a preserved partition given an imprimitive group action

[Matan Ziv-Av]

On Sun, 10 Jun 2012, Nathann Cohen wrote:

> Here it is : I have a permutation group G, or a group acting on a set of
> vertices in a graph, which sometime turns out to be imprimitive [1], which
> means (I learned that recently) that there exists a nontrivial partition P
> = P1, ... P_k of my set of vertices such that the  image of any P_i by an
> element of G is another element of P. I do not know yet whether GAP can
> tell me whether a given permutation group is primitive, but more than that
> I would be interested in obtaining -- when it is not the case -- an example
> of partition which is preserved in such a way.
> Actually, because I am *very* greedy, I would ideally like to obtain an
> inclusionwise "finest" (or smallest) partition, and in an ideal world to
> enumerate them all.
>
> May it be a task that GAP can solve ? :-)

The function Blocks is relevant (see also AllBlocks and MaximalBlocks).

See here: http://www.gap-system.org/Manuals/doc/htm/ref/CHAP039.htm#SECT010


-- 
Matan Ziv-Av.                         matan at svgalib.org