On Thursday, January 9, 2014 9:44:57 AM UTC-5, Georgi Guninski wrote:
>
> Strange results with subgroups of automorphism group of graphs
>
> There is an element in the automorphism group of graph
> which is in no subgroup (though the full group is a subgroup).
>
> I suspect the problem is the usage of zero.
>
> G1=Graph(':H`ECw@HGXGAGUG`e');G=G1.automorphism_group();sg=G.subgroups()
> print G.gens()
> [(0,7)(1,4)(2,3)(6,8)]
> print sg
> [Permutation Group with generators [()], Permutation Group with
> generators [(1,8)(2,5)(3,4)(7,9)]]
>
>
sage: G.gens()
[(0,7)(1,4)(2,3)(6,8)]
sage: [s.gens() for s in sg]
[[()], [(1,8)(2,5)(3,4)(7,9)]]
Yeah, that's a problem. At least we get
sage: G.is_isomorphic(sg[0])
False
sage: G.is_isomorphic(sg[1])
True
which is trivial but I think it confirms your suspicion. We seem to have
Gap-style numbering in the subgroups and Sage/Python-style numbering in the
group itself. Here's the code:
all_sg = []
ccs = self._gap_().ConjugacyClassesSubgroups()
for cc in ccs:
for h in cc.Elements():
all_sg.append(PermutationGroup(gap_group=h))
return all_sg
So we send self to Gap...
sage: G._gap_()
Group( [ (1,8)(2,5)(3,4)(7,9) ] )
sage: G
Permutation Group with generators [(0,7)(1,4)(2,3)(6,8)]
There we go.
Beezer, you apparently wrote this... how would you recommend fixing this?
I'll open a Trac ticket momentarily.
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