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. ma...@svgalib.org
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