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- Ascendant_subgroup abstract "In mathematics, in the field of group theory, a subgroup of a group is said to be ascendant if there is an ascending series starting from the subgroup and ending at the group, such that every term in the series is a normal subgroup of its successor.The series may be infinite. If the series is finite, then the subgroup is subnormal. Here are some properties of ascendant subgroups: Every subnormal subgroup is ascendant; every ascendant subgroup is serial. In a finite group, the properties of being ascendant and subnormal are equivalent. An arbitrary intersection of ascendant subgroups is ascendant. Given any subgroup, there is a minimal ascendant subgroup containing it.".
- Ascendant_subgroup wikiPageID "4966647".
- Ascendant_subgroup wikiPageLength "1250".
- Ascendant_subgroup wikiPageOutDegree "10".
- Ascendant_subgroup wikiPageRevisionID "491048013".
- Ascendant_subgroup wikiPageWikiLink Category:Subgroup_properties.
- Ascendant_subgroup wikiPageWikiLink Descendant_subgroup.
- Ascendant_subgroup wikiPageWikiLink Group_(mathematics).
- Ascendant_subgroup wikiPageWikiLink Group_theory.
- Ascendant_subgroup wikiPageWikiLink Mathematics.
- Ascendant_subgroup wikiPageWikiLink Normal_subgroup.
- Ascendant_subgroup wikiPageWikiLink Serial_subgroup.
- Ascendant_subgroup wikiPageWikiLink Springer-Verlag.
- Ascendant_subgroup wikiPageWikiLink Springer_Science+Business_Media.
- Ascendant_subgroup wikiPageWikiLink Subgroup.
- Ascendant_subgroup wikiPageWikiLink Subnormal_subgroup.
- Ascendant_subgroup wikiPageWikiLinkText "Ascendant subgroup".
- Ascendant_subgroup wikiPageWikiLinkText "ascendant subgroup".
- Ascendant_subgroup wikiPageWikiLinkText "ascendant".
- Ascendant_subgroup hasPhotoCollection Ascendant_subgroup.
- Ascendant_subgroup wikiPageUsesTemplate Template:Abstract-algebra-stub.
- Ascendant_subgroup wikiPageUsesTemplate Template:Cite_book.
- Ascendant_subgroup subject Category:Subgroup_properties.
- Ascendant_subgroup hypernym Series.
- Ascendant_subgroup type TelevisionShow.
- Ascendant_subgroup type Property.
- Ascendant_subgroup comment "In mathematics, in the field of group theory, a subgroup of a group is said to be ascendant if there is an ascending series starting from the subgroup and ending at the group, such that every term in the series is a normal subgroup of its successor.The series may be infinite. If the series is finite, then the subgroup is subnormal. Here are some properties of ascendant subgroups: Every subnormal subgroup is ascendant; every ascendant subgroup is serial.".
- Ascendant_subgroup label "Ascendant subgroup".
- Ascendant_subgroup sameAs m.0cxk8m.
- Ascendant_subgroup sameAs Q4803805.
- Ascendant_subgroup sameAs Q4803805.
- Ascendant_subgroup wasDerivedFrom Ascendant_subgroup?oldid=491048013.
- Ascendant_subgroup isPrimaryTopicOf Ascendant_subgroup.