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- Perfect_core abstract "In mathematics, in the field of group theory, the perfect core (or perfect radical) of a group is its largest perfect subgroup. Its existence is guaranteed by the fact that the subgroup generated by a family of perfect subgroups is again a perfect subgroup. The perfect core is also the point where the transfinite derived series stabilizes for any group.A group whose perfect core is trivial is termed a hypoabelian group. Every solvable group is hypoabelian, and so is every free group. More generally, every residually solvable group is hypoabelian.The quotient of a group G by its perfect core is hypoabelian, and is called the hypoabelianization of G.".
- Perfect_core wikiPageID "4939190".
- Perfect_core wikiPageLength "977".
- Perfect_core wikiPageOutDegree "14".
- Perfect_core wikiPageRevisionID "550798333".
- Perfect_core wikiPageWikiLink Category:Functional_subgroups.
- Perfect_core wikiPageWikiLink Category:Group_theory.
- Perfect_core wikiPageWikiLink Category:Solvable_groups.
- Perfect_core wikiPageWikiLink Commutator_subgroup.
- Perfect_core wikiPageWikiLink Free_group.
- Perfect_core wikiPageWikiLink Generating_set_of_a_group.
- Perfect_core wikiPageWikiLink Group_(mathematics).
- Perfect_core wikiPageWikiLink Group_theory.
- Perfect_core wikiPageWikiLink Mathematics.
- Perfect_core wikiPageWikiLink Perfect_group.
- Perfect_core wikiPageWikiLink Quotient_group.
- Perfect_core wikiPageWikiLink Residual_property_(mathematics).
- Perfect_core wikiPageWikiLink Residually_solvable_group.
- Perfect_core wikiPageWikiLink Solvable_group.
- Perfect_core wikiPageWikiLink Subgroup.
- Perfect_core wikiPageWikiLink Transfinite_derived_series.
- Perfect_core wikiPageWikiLinkText "Perfect core".
- Perfect_core wikiPageWikiLinkText "perfect core".
- Perfect_core hasPhotoCollection Perfect_core.
- Perfect_core wikiPageUsesTemplate Template:Abstract-algebra-stub.
- Perfect_core wikiPageUsesTemplate Template:Unreferenced.
- Perfect_core subject Category:Functional_subgroups.
- Perfect_core subject Category:Group_theory.
- Perfect_core subject Category:Solvable_groups.
- Perfect_core type Article.
- Perfect_core type Group.
- Perfect_core type Article.
- Perfect_core type Group.
- Perfect_core comment "In mathematics, in the field of group theory, the perfect core (or perfect radical) of a group is its largest perfect subgroup. Its existence is guaranteed by the fact that the subgroup generated by a family of perfect subgroups is again a perfect subgroup. The perfect core is also the point where the transfinite derived series stabilizes for any group.A group whose perfect core is trivial is termed a hypoabelian group. Every solvable group is hypoabelian, and so is every free group.".
- Perfect_core label "Perfect core".
- Perfect_core sameAs صميم_مثالي_(رياضيات).
- Perfect_core sameAs m.0cw427.
- Perfect_core sameAs Q11246145.
- Perfect_core sameAs Q11246145.
- Perfect_core wasDerivedFrom Perfect_core?oldid=550798333.
- Perfect_core isPrimaryTopicOf Perfect_core.