# Permutation group: (1234)=(12)(13)(14)

 0 How do I show in sage that  (1234)=(12)(13)(14)  I tried make use of:  PermutationGroup([1,2]) * PermutationGroup([1,3])  but it doesn't do what is needed. asked Jun 12 '12 bk322 53 ● 2 ● 10

 2 Sage's built-in help is useful here. sage: PermutationGroup? Definition: PermutationGroup(gens=None, gap_group=None, domain=None, canonicalize=True, category=None) Docstring: Return the permutation group associated to x (typically a list of generators). INPUT: * "gens" - list of generators (default: "None") * "gap_group" - a gap permutation group (default: "None") * "canonicalize" - bool (default: "True"); if "True", sort generators and remove duplicates OUTPUT: * A permutation group.  So indeed you get a permutation group, with these things as generators. You can't multiply groups. A similar look at help will show you that Permutation does not give an element of a group, though you can convert an element of such a group to one. But you can get group elements from your group. Try this. sage: G = SymmetricGroup(4) sage: G([(1,2)]) (1,2) sage: G([(1,2)])*G([(1,3)])*G([(1,4)]) (1,2,3,4)  posted Jun 12 '12 kcrisman 6784 ● 14 ● 67 ● 152 2Permutation((1,2)) * Permutation((1,3)) * Permutation((1,4)) == Permutation((1,2,3,4)) should also work.DSM (Jun 12 '12)1Good point, but I don't think they'll be group elements, will they? Well, it's somewhat a semantic issue anyway until one starts using the actual methods of these classes.kcrisman (Jun 12 '12)

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