Subgroups of automorphism groups of graphs

[Peter Mueller]

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

[Gareth Ma]

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.

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[dmo...@deductivepress.ca]

These examples reveal a bug in the commutator method --- it ignores the domain of the permutation group.  I have opened .github issue #39416 for this.