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- Engel_group abstract "In mathematics, an element x of a Lie group or a Lie algebra is called an n-Engel element, named after Friedrich Engel, if it satisfies the n-Engel condition that the repeated commutator [...[[x,y],y], ..., y] with n copies of y is trivial (where [x, y] means xyx−1y−1 or the Lie bracket). It is called an Engel element if it satisfies the Engel condition that it is n-Engel for some n.A Lie group or Lie algebra is said to satisfy the Engel or n-Engel conditions if every element does. Such groups or algebras are called Engel groups, n-Engel groups, Engel algebras, and n-Engel algebras.Every nilpotent group or Lie algebra is Engel. Engel's theorem states that every finite-dimensional Engel algebra is nilpotent. (Cohn 1955) gave examples of a non-nilpotent Engel groups and algebras.".
- Engel_group wikiPageID "17228297".
- Engel_group wikiPageLength "1750".
- Engel_group wikiPageOutDegree "10".
- Engel_group wikiPageRevisionID "604259284".
- Engel_group wikiPageWikiLink Category:Group_theory.
- Engel_group wikiPageWikiLink Category:Lie_algebras.
- Engel_group wikiPageWikiLink Engel_identity.
- Engel_group wikiPageWikiLink Engels_theorem.
- Engel_group wikiPageWikiLink Friedrich_Engel_(mathematician).
- Engel_group wikiPageWikiLink Lie_algebra.
- Engel_group wikiPageWikiLink Lie_group.
- Engel_group wikiPageWikiLink Mathematics.
- Engel_group wikiPageWikiLink Nilpotent_group.
- Engel_group wikiPageWikiLinkText "Engel group".
- Engel_group wikiPageUsesTemplate Template:Citation.
- Engel_group wikiPageUsesTemplate Template:Harv.
- Engel_group wikiPageUsesTemplate Template:Reflist.
- Engel_group subject Category:Group_theory.
- Engel_group subject Category:Lie_algebras.
- Engel_group type Algebra.
- Engel_group comment "In mathematics, an element x of a Lie group or a Lie algebra is called an n-Engel element, named after Friedrich Engel, if it satisfies the n-Engel condition that the repeated commutator [...[[x,y],y], ..., y] with n copies of y is trivial (where [x, y] means xyx−1y−1 or the Lie bracket). It is called an Engel element if it satisfies the Engel condition that it is n-Engel for some n.A Lie group or Lie algebra is said to satisfy the Engel or n-Engel conditions if every element does.".
- Engel_group label "Engel group".
- Engel_group sameAs Q5377481.
- Engel_group sameAs m.043kzbq.
- Engel_group sameAs Q5377481.
- Engel_group wasDerivedFrom Engel_group?oldid=604259284.
- Engel_group isPrimaryTopicOf Engel_group.