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The query [[Category:Analogues in Lie rings of facts about groups]] was answered by the SMWSQLStore3 in 0.0079 seconds.


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 Analogue of
Analogue of critical subgroup theorem for nilpotent Lie ringsThompson's critical subgroup theorem
Centralizer-free ideal implies automorphism-faithfulNormal and centralizer-free implies automorphism-faithful
Centralizer-free ideal implies derivation-faithfulNormal and centralizer-free implies automorphism-faithful
Characteristicity is transitive for Lie ringsCharacteristicity is transitive
Derivation-invariance does not satisfy intermediate subring conditionCharacteristicity does not satisfy intermediate subgroup condition
Derivation-invariance is Lie bracket-closedCharacteristicity is commutator-closed
Derivation-invariance is centralizer-closedCharacteristicity is centralizer-closed
Derivation-invariance is not upper join-closedCharacteristicity is not upper join-closed
Derivation-invariance is transitiveCharacteristicity is transitive
Derivation-invariant subring of ideal implies idealCharacteristic of normal implies normal
Ideal not implies derivation-invariantNormal not implies characteristic
Ideal property is not transitive for Lie ringsNormality is not transitive
Inner derivation implies endomorphism for class two Lie ringClass two implies commutator map is endomorphism
Left transiter of ideal is derivation-invariant Lie subringLeft transiter of normal is characteristic
Maximal among abelian ideals implies self-centralizing in nilpotent Lie ringMaximal among abelian normal implies self-centralizing in nilpotent
Multiplication by n map is an endomorphism iff derived subring has exponent dividing n(n-1)N-abelian iff abelian (if order is relatively prime to n(n-1))