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- A '''nilpotent group''' can be thought of a group that is only finitely removed from an [[ == Characterization and Properties of Nilpotent Groups ==9 KB (1,768 words) - 16:55, 5 June 2008
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- A group <math>G</math> is called [[nilpotent group |nilpotent]] if <math>C^n(G)</math> is the [[trivial group]] for sufficiently large <m * [[Nilpotent group]]3 KB (577 words) - 00:24, 1 June 2008
- A '''nilpotent group''' can be thought of a group that is only finitely removed from an [[ == Characterization and Properties of Nilpotent Groups ==9 KB (1,768 words) - 16:55, 5 June 2008
- ...it is solvable of class at most <math>n</math>. Thus if <math>G</math> is nilpotent, then it is solvable; however, the converse is not generally true.2 KB (393 words) - 00:13, 2 June 2008
- Every [[nilpotent group]] is solvable. In particular, if a group is nilpotent of class at most <math>2^n-1</math>, then it is solvable of class at most < But it is not nilpotent: the terms of its [[lower central series]] are4 KB (711 words) - 16:04, 5 June 2008
- '''Corollary 1.''' Every <math>p</math>-group is [[nilpotent group |nilpotent]]. This is a property of nilpotent groups in general.4 KB (814 words) - 21:50, 3 November 2023
- * [[Nilpotent group]]11 KB (2,071 words) - 11:25, 9 April 2019
- ...ntries such that either A or B commutes with C = AB - BA. Prove that C is nilpotent, i.e. C^k = 0 for some integer k22 KB (3,358 words) - 14:17, 18 July 2017
- Let <math>A</math> be a [[commutative ring]]. The set of all [[nilpotent]] elements of <math>A</math> (i.e., the set of all <math>x</math> for which ...\in \mathfrak{p}</math>. (Such an integer exists, since <math>x</math> is nilpotent.) Suppose that <math>n>1</math>. Then <math>x \cdot x^{n-1} \in \mathfrak3 KB (532 words) - 11:14, 20 September 2008
- is either [[invertible]] or [[nilpotent]].2 KB (263 words) - 20:00, 19 April 2012