These examples reveal a bug in the commutator method --- it ignores the
domain of the permutation group. I have opened .github issue #39416
<https://github.com/sagemath/sage/issues/39416> for this.
On Tuesday, January 28, 2025 at 3:43:56 AM UTC-7 grh...@gmail.com wrote:
> It seems that this is intended? The correct equivalent code is:
>
> sage: gens = [[(2, 4)], [(1, 2)]]
> sage: pg = PermutationGroup(gens=gens); pg
> Permutation Group with generators [(2,4), (1,2)]
> sage: pg._libgap_()
> Group([ (2,4), (1,2) ])
> sage: pg = PermutationGroup(gens=gens, domain={1, 2, 4}); pg
> Permutation Group with generators [(2,4), (1,2)]
> sage: pg._libgap_()
> Group([ (2,3), (1,2) ])
>
> Which is what's done at
>
> https://github.com/sagemath/sage/blob/develop/src/sage/graphs/generic_graph.py#L24161-L24170
> .
> But I'm not an expert in this part of the code.
>
> Also, I didn't know we have a 25k lines file.
>
> On 1/28/25 10:27 AM, 'Peter Mueller' via sage-devel wrote:
> > The following code shows that subgroups of automorphism groups of graphs
> are
> > handled wrongly:
> >
> > sage: g = Graph([[1, 2, 4], []])
> > sage: a = g.automorphism_group()
> > sage: print(a)
> > Permutation Group with generators [(2,4), (1,2)]
> > sage: print(a.commutator())
> > Permutation Group with generators [(1,2,3)]
> >
> > Note that a.commutator() moves 3 though 3 is not a vertex of the graph.
> > Somewhat strangely, if one defines directly a = PermutationGroup([[(2,
> 4)], [(1,
> > 2)]]), then a.commutator() returns the correct subgroup.
> >
> > By the way, it doesn't help if the n vertices of the graph consist of
> the list
> > [1..n]. I have a complicated example where the automorphism group is
> computed
> > correctly, but the action of the commutator subgroup is with respect to a
> > different labeling of the vertices.
> >
> > -- Peter Mueller
> >
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