Permutation groups#
- class sage.categories.permutation_groups.PermutationGroups#
Bases:
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
- Finite#
alias of
FinitePermutationGroups
- super_categories()#
Return a list of the immediate super categories of
self
.EXAMPLES:
sage: PermutationGroups().super_categories() [Category of groups]