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Computing permutations

asked 2013-12-03 09:41:38 -0500

anonymous user

Anonymous

Is there a way to solve the following question is Sage? I have symmetric group $S_8$ and its elements $a=(x_1 x_2)(x_3 x_4),b=(x_5 x_6), c=(x_7 x_8)(x_9 x_{10})(x_{11} x_{12})(x_{13} x_{14})$ Here of course we might have $x_i=x_j$ if $i\ne j$. Is some given $(y_1 y_2)\in \langle a,b,c\rangle$?

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answered 2013-12-04 03:33:19 -0500

ppurka gravatar image

You can use the PermutationGroup to create a permutation group from specific elements (cycle notation). And then you can check if a particular element is in the group:

sage: G = PermutationGroup([[(1,2,3),(4,5)],[(3,4)]])
sage: G
Permutation Group with generators [(3,4), (1,2,3)(4,5)]
sage: (3,4) in G
True
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Asked: 2013-12-03 09:41:38 -0500

Seen: 59 times

Last updated: Dec 04 '13