### Navigation

- index
- modules |
- next |
- previous |
- Category Theory »

# Permutation groups

class `sage.categories.permutation_groups.``PermutationGroups`(s=None)

  Bases: `sage.categories.category.Category`

  The category of permutation groups.

  A permutation group is a group whose elements are concretely represented by permutations of some set. In other words, the group comes endowed with a distinguished action on some set.

  This distinguished action should be preserved by permutation group morphisms. For details, see Wikipedia article Permutation_group#Permutation_isomorphic_groups.

  Todo

  shall we accept only permutations with finite support or not?

  EXAMPLES:

      sage: PermutationGroups()
      Category of permutation groups
      sage: PermutationGroups().super_categories()
      [Category of groups]

  The category of permutation groups defines additional structure that should be preserved by morphisms, namely the distinguished action:

      sage: PermutationGroups().additional_structure()
      Category of permutation groups

  TESTS:

      sage: C = PermutationGroups()
      sage: TestSuite(C).run()

  `Finite`

    alias of `FinitePermutationGroups`

  `super_categories`()

    Return a list of the immediate super categories of `self`.

    EXAMPLES:

        sage: PermutationGroups().super_categories()
        [Category of groups]

### Navigation

- index
- modules |
- next |
- previous |
- Category Theory »