# Permutation groups¶

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

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]


#### Previous topic

Partially ordered monoids

Pointed sets