en>David Eppstein: remove orphan tag

2013-11-13T05:28:55Z

remove orphan tag

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			{{ref improve\|date=June 2012}}
			The '''Engel identity''', named after [[Friedrich Engel (mathematician)\|Friedrich Engel]], is a mathematical equation that is satisfied by all elements of a [[Lie ring]], in the case of an Engel Lie ring, or by all the elements of a [[group (mathematics)\|group]], in the case of an [[Engel group]]. The Engel identity is the defining condition of an [[Engel group]].

			== Formal definition ==
			A [[Lie ring]] <math>L</math> is defined as a [[nonassociative ring]] with multiplication that is [[anticommutative]] and satisfies the [[Jacobi identity]] with respect to the [[Commutator\|Lie bracket]] <math>[x,y]</math>, defined for all elements <math>x,y</math> in the ring <math>L</math>. The Lie ring <math>L</math> is defined to be an n-Engel Lie ring if and only if
			* for all <math>x, y</math> in <math>L</math>, the n-Engel identity
			<math> [x,[x, \ldots, [x,[x,y]],\ldots]] = 0</math> (n copies of <math>x</math>), is satisfied.<ref>{{cite journal\|title=Engel Lie-Algebras\|last=Traustason\|first=Gunnar\|journal=Quart. J. Math. Oxford\|year=1993\|volume=44\|issue=3\|pages=355–384\|doi=10.1093/qmath/44.3.355}}</ref>

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Study your circumstances. This may place you in the best situation to be successful.<br><br>Even though a legal representative is technically certified doesn't necessarily indicate you should work together with them. Their professional [http://~~www~~.~~youtube.com~~/~~watch?v~~=~~A4NiEiCwUA0 www.youtube.com/watch?v~~=~~A4NiEiCwUA0] abilities are crucial, but bear in mind you will have to pay significant amounts~~ of ~~time collaborating using them. Points will probably be easier if you can get as well as your legal representative.<br><br>You will feel great with~~ a ~~decent legal professional that will help you together with your scenario. Due to this informative article, you~~'~~ll be able to get a lawyer to protect you. Remember the following tips when you begin deciding on one.~~		In the case of a [[group (mathematics)\|group]] <math>G</math>, in the preceding definition, use the definition {{nowrap\|[''x'',''y''] {{=}} ''x''<sup>−1</sup> • ''y''<sup>−1</sup> • ''x'' • ''y''}} and replace <math>0</math> by <math>1</math>, where <math>1</math> is the identity element of the group <math>G</math>.<ref>{{cite journal\|title=Engel groups (a survey)\|author=Traustason, Gunnar\|url=http://www.groupsstandrews.org/2009/Talks/Traustason.pdf}}</ref>

			==See also==
			* [[Adjoint representation of a Lie group\|Adjoint representation]]
			* [[Efim Zelmanov]]
			* [[Engel's theorem]]

			==References==
			{{reflist}}


			[[Category:Group theory]]
			[[Category:Lie algebras]]

en>Dekart: removed Category:Mathematics; added Category:Quadrilaterals using HotCat

2012-09-01T08:22:13Z

removed Category:Mathematics; added Category:Quadrilaterals using HotCat

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Perpendicular bisector construction - Revision history

en>David Eppstein: remove orphan tag

en>Dekart: removed Category:Mathematics; added Category:Quadrilaterals using HotCat