Permutation groups¶
- class sage.categories.permutation_groups.PermutationGroups[source]¶
- 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] - >>> from sage.all import * >>> PermutationGroups() Category of permutation groups >>> 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 - >>> from sage.all import * >>> PermutationGroups().additional_structure() Category of permutation groups - Finite[source]¶
- alias of - FinitePermutationGroups