Hi William,

On Apr 1, 8:28 pm, William Stein <[email protected]> wrote:
> This is absolutely definitely, without any question, a huge bug.  Open
> a trac ticket!

It is #5664.

And I found that things are much worse:

1.
sage: G2=G.subgroup([G((1,2,3,4)),G((1,2))])
sage: G==G2
True
sage: G2==G
Traceback (most recent call last):
...
AttributeError: 'SymmetricGroup' object has no attribute
'ambient_group'

Hence, == is not a symmetric relation, and __cmp__ raises an error
(which, afaik, must not be the case according to Python
specification).

2.
sage: G=SymmetricGroup(6)
sage: G1=G.subgroup([G((1,2,3,4,5)),G((1,2))])
sage: G2=G.subgroup([G((1,2,3,4)),G((1,2))])
sage: K=G2.subgroup([G1((1,2,3))])
sage: H=G1.subgroup([G2(())])
sage: H<K
False
sage: K<H
True

Hence, the trivial group in G1 is considered greater than a non-
trivial group in G2, because G1>G2.
Is this really what cmp should do for subgroups?

Yours,
   Simon

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