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The query [[Fact about.Page::Powering-invariant subgroup]] was answered by the SMWSQLStore3 in 0.0094 seconds.

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C-closed implies powering-invariant, Characteristic not implies powering-invariant in solvable group, Characteristic subgroup of abelian group implies powering-invariant, Divisibility-closed implies powering-invariant, Endomorphism image implies powering-invariant, Every normal subgroup satisfies the quotient-to-subgroup powering-invariance implication, Finite implies powering-invariant, Finite index implies powering-invariant, Minimal normal implies powering-invariant in solvable group, Powering-invariance does not satisfy intermediate subgroup condition, Powering-invariance does not satisfy lower central series condition in nilpotent group, Powering-invariance is centralizer-closed, Powering-invariance is commutator-closed in nilpotent group, Powering-invariance is not commutator-closed, Powering-invariance is not finite-join-closed, Powering-invariance is not quotient-transitive, Powering-invariance is strongly intersection-closed, Powering-invariance is strongly join-closed in nilpotent group, Powering-invariance is transitive, Powering-invariance is union-closed, Powering-invariant not implies divisibility-closed, Powering-invariant not implies local powering-invariant, Socle is powering-invariant in solvable group, Subgroup of abelian group not implies powering-invariant