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- Fully_characteristic_subgroup abstract "In mathematics, a subgroup of a group is fully characteristic (or fully invariant) if it is invariant under every endomorphism of the group.Every group has itself (the improper subgroup) and the trivial subgroup as two of its fully characteristic subgroups. Every fully characteristic subgroup is a strictly characteristic subgroup, and a fortiori a characteristic subgroup.The commutator subgroup of a group is always a fully characteristic subgroup. More generally, any verbal subgroup is always fully characteristic. For any reduced free group, and, in particular, for any free group, the converse also holds — every fully characteristic subgroup is verbal.See also characteristic subgroup.".
- Fully_characteristic_subgroup wikiPageID "2774363".
- Fully_characteristic_subgroup wikiPageLength "1215".
- Fully_characteristic_subgroup wikiPageOutDegree "13".
- Fully_characteristic_subgroup wikiPageRevisionID "678283072".
- Fully_characteristic_subgroup wikiPageWikiLink Category:Subgroup_properties.
- Fully_characteristic_subgroup wikiPageWikiLink Characteristic_subgroup.
- Fully_characteristic_subgroup wikiPageWikiLink Commutator_subgroup.
- Fully_characteristic_subgroup wikiPageWikiLink Endomorphism.
- Fully_characteristic_subgroup wikiPageWikiLink Free_group.
- Fully_characteristic_subgroup wikiPageWikiLink Group_(mathematics).
- Fully_characteristic_subgroup wikiPageWikiLink Invariant_(mathematics).
- Fully_characteristic_subgroup wikiPageWikiLink Mathematics.
- Fully_characteristic_subgroup wikiPageWikiLink Reduced_free_group.
- Fully_characteristic_subgroup wikiPageWikiLink Subgroup.
- Fully_characteristic_subgroup wikiPageWikiLink Verbal_subgroup.
- Fully_characteristic_subgroup wikiPageWikiLinkText "Fully characteristic subgroup".
- Fully_characteristic_subgroup wikiPageWikiLinkText "fully characteristic subgroup".
- Fully_characteristic_subgroup wikiPageWikiLinkText "fully characteristic".
- Fully_characteristic_subgroup wikiPageUsesTemplate Template:Cite_book.
- Fully_characteristic_subgroup subject Category:Subgroup_properties.
- Fully_characteristic_subgroup hypernym Invariant.
- Fully_characteristic_subgroup type Property.
- Fully_characteristic_subgroup comment "In mathematics, a subgroup of a group is fully characteristic (or fully invariant) if it is invariant under every endomorphism of the group.Every group has itself (the improper subgroup) and the trivial subgroup as two of its fully characteristic subgroups. Every fully characteristic subgroup is a strictly characteristic subgroup, and a fortiori a characteristic subgroup.The commutator subgroup of a group is always a fully characteristic subgroup.".
- Fully_characteristic_subgroup label "Fully characteristic subgroup".
- Fully_characteristic_subgroup sameAs Q5508339.
- Fully_characteristic_subgroup sameAs m.081znp.
- Fully_characteristic_subgroup sameAs Q5508339.
- Fully_characteristic_subgroup wasDerivedFrom Fully_characteristic_subgroup?oldid=678283072.
- Fully_characteristic_subgroup isPrimaryTopicOf Fully_characteristic_subgroup.