Need to shift a permutation (1,2,3)(4,5)->(6,7,8)(9,10)

permutation

asked 2016-02-08 17:25:37 +0200

So I've been trying to shift a permutation group upwards to be able to make a cartesian product of two arbitrary permutation groups into a permutation group. My idea was to simply shift one permutation group up enough so that it commutes with the other. However I am stuck trying to figure out how to shift it up, i.e. add 5 to each number in the permutation. Anyone have any ideas?

Thanks

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answered 2016-02-08 20:41:08 +0200

vdelecroix
7397 ●19 ●81 ●164 http://www.labri.fr/pe...

You can simply use conjugation

sage: S5 = SymmetricGroup(5)
sage: S10 = SymmetricGroup(10)
sage: t = S10("(1,6)(2,7)(3,8)(4,9)(5,10)")
sage: s = S5("(1,2,3)(4,5)")
sage: t*s*~t
(6,7,8)(9,10)

Or be more direct with

sage: f = lambda s: S10(range(1,6) + [s(i)+5 for i in range(1,6)])
sage: f(s)
(6,7,8)(9,10)

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Asked: 2016-02-08 17:25:37 +0200

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Last updated: Feb 08 '16

Need to shift a permutation (1,2,3)(4,5)->(6,7,8)(9,10) edit

1 Answer