# nilpotent

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## nilpotent

[¦nil′pōt·ənt]
(mathematics)
An element of some algebraic system which vanishes when raised to a certain power.
References in periodicals archive ?
The elements of this semigroup will be called affine maps, since aff (G) is merely a generalization of the semigroup of affine maps aff([R.sup.n]) to the nilpotent case.
[K.sub.0](x)--the set of all nilpotent elements of K(x);
There are ten chapters: Preliminaries, Sylow theory, Solvable groups and nilpotent groups, Group extensions, Hall subgroups, Frobenius groups, Transfer, Characters, Finite subgroups of GLn, and Small groups.
(viii) In 2005, Mahalanobis  did not discriminate the D-H key exchange protocol from a cyclic group to a finitely presented nonabelian nilpotent group of class 2.
Then [S.sup.(*).sub.j,1] = [R.sup.(*).sub.j][S.sup.(*).sub.j,2] where [R.sup.(*).sub.j,1]is a nilpotent operator such that
In particular, if A is nilpotent, then system (2) and (3) is null output controllable.
where C(t) is invertible and N(t) is nilpotent of index k.
(ii) An element a [member of] NQR is called nilpotent if there exists n [member of] [Z.sup.+] such that [a.sup.n] = 0.
In the algebra of split octonions two types of primitive zero divisors, idempotent elements (projection operators) and nilpotent elements (Grassmann numbers), can be constructed [1,10].
Recall that a bounded linear operator N is quasinilpotent if the spectrum of N is identical to 0 and N is nilpotent if there is a positive integer k such that [N.sup.k] = 0.
* [[H.sub.n], [H.sub.n]] = Z = [PHI]([H.sub.n]) and [H.sub.n] is nilpotent of class 2 ([PHI]([H.sub.n]) is the Frattini subgroup of H, that is, the intersection of all its maximal subgroups).

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