Dear Jim,
On May 15, 4:03 am, jimfar <[email protected]> wrote:
> Thanks, I was confusing myself with the definition of the order of an
> element with order of the cycle.
Are you really confusing it?
As much as I understood, you only want those elements that have a
single (!) cycle of length 3. Then, order() is the wrong thing to ask
for!
sage: G=PermutationGroup([((1,2,3),(4,5,6))])
sage: G.0
(1,2,3)(4,5,6)
sage: G.0.order()
3
So, G.0 is not a 3-cycle, but it is of order 3.
I don't know if there is better way to test the number of cycles, but
you could do:
[x for x in AlternatingGroup(5) if x.order()==3 and len(x.cycles())
==1]
The difference becomes apparent when you do it for AlternatingGroup
(6), rather than AlternatingGroup(5).
Cheers,
Simon
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