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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 wikiPageRevisionID "550798333".
- Perfect_core hasPhotoCollection Perfect_core.
- Perfect_core subject Category:Functional_subgroups.
- Perfect_core subject Category:Group_theory.
- Perfect_core subject Category:Solvable_groups.
- Perfect_core type Abstraction100002137.
- Perfect_core type FunctionalSubgroups.
- Perfect_core type Group100031264.
- Perfect_core type SolvableGroups.
- Perfect_core type Subgroup108001083.
- 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 label "صميم مثالي (رياضيات)".
- Perfect_core sameAs m.0cw427.
- Perfect_core sameAs Q11246145.
- Perfect_core sameAs Q11246145.
- Perfect_core sameAs Perfect_core.
- Perfect_core wasDerivedFrom Perfect_core?oldid=550798333.
- Perfect_core isPrimaryTopicOf Perfect_core.