In algebraic topology, the nilpotence theorem gives a condition for an element in the homotopy groups of a ring spectrum to be nilpotent, in terms of the...

the seven conjectures, then the nilpotence conjecture, was proved in 1988 and is now known as the nilpotence theorem. The telescope conjecture, which...

^{\infty }} of C P ∞ {\displaystyle \mathbb {CP} ^{\infty }} . The nilpotence theorem states that, for any ring spectrum R {\displaystyle R} , the kernel...

{\displaystyle {\mathfrak {N}}} ; this is a consequence of the binomial theorem. This ideal is the nilradical of the ring. Every nilpotent element x {\displaystyle...

in the stable homotopy category than you might think. For example, the nilpotence conjecture states that some suspension of some iteration of a map between...

VIII, §11, Prop. 2) Jacobson (1979, Ch. III, §11, Theorem 17) André, Yves; Kahn, Bruno (2002), "Nilpotence, radicaux et structures monoïdales", Rend. Semin...

sequence Chromatic homotopy theory Equivariant stable homotopy theory Nilpotence theorem Serre, Jean-Pierre (1953). "Groupes d'homotopie et classes de groupes...

element of non-zero degree is nilpotent; the nilpotence theorem on complex cobordism implies Nishida's theorem.[citation needed] Example: If η is the generator...

pseudo-abelian additive categories. See for example Yves André, Bruno Kahn: Nilpotence, radicaux et structures monoïdales. With an appendix by Peter O'Sullivan...

Jordan normal form, up to a permutation of the Jordan blocks Index of nilpotence Elementary divisors, which form a complete set of invariants for similarity...

*-algebras. p. 1283. For the term, compare Engel's theorem, also on nilpotency. Bechtell (1971), p. 51, Theorem 5.1.3 Isaacs (2008), Thm. 1.26 Bechtell, Homer...

France, ISBN 978-2-85629-164-1, MR 2115000 Voevodsky, V. (1995), "A nilpotence theorem for cycles algebraically equivalent to 0", Int. Math. Res. Notices...

the 2-groups of maximal class, that is those groups of order 2n+1 and nilpotency class n. The iterated wreath products of cyclic groups of order p are...

work on Thom spectra. This work was used heavily in the proof of the nilpotence theorem by Ethan Devinatz, Michael J. Hopkins, and Jeffrey Smith. In 1998...

Hovey-Strickland, "Morava K-theory and localisation" Ravenel, Douglas C. (1992), Nilpotence and periodicity in stable homotopy theory, Annals of Mathematics Studies...

p-nilpotence and various non-simplicity criteria focussing on showing that a finite group has a normal subgroup of index p. The focal subgroup theorem relates...

Notes 117, Cambridge Univ. Press, Cambridge, 1987 V. Voevodsky, A nilpotence theorem for cycles algebraically equivalent to zero. Internat. Math. Res....

particularly important, since it is an example of a 2-group of maximal nilpotency class. In Bertram Huppert's text Endliche Gruppen, this group is called...

matrix defined as Nij = δi,j−1 (where δ is the Kronecker delta). The nilpotency of N can be exploited when calculating f(A) where f is a complex analytic...

we will not prove here. A somewhat easier equivalent condition for the nilpotency of g {\displaystyle {\mathfrak {g}}}  : g {\displaystyle {\mathfrak {g}}}...

Both of these concepts are special cases of a more general concept of nilpotence that applies to elements of rings. The matrix A = [ 0 1 0 0 ] {\displaystyle...

(x_{n})=\pi (x)_{n}} . The Jordan decomposition can be used to characterize nilpotency of an endomorphism. Let k be an algebraically closed field of characteristic...

classified up to conjugacy (in GL(n, C)) by eigenvalues and nilpotence (concretely, nilpotence means where 1s occur in the Jordan blocks). Thus elements...

exclusively with finite groups. The nilpotency of the Fitting subgroup of a finite group is guaranteed by Fitting's theorem which says that the product of...

In mathematics, specifically the theory of Lie algebras, Lie's theorem states that, over an algebraically closed field of characteristic zero, if π :...

Witten genus and the theorem of the cube. Invent. Math. 146 (2001), no. 3, 595–687. (with Matthew Ando and Neil Strickland) Nilpotence and stable homotopy...

, {\displaystyle V=\bigoplus _{n>0}V^{n},} satisfying the following "nilpotence condition" on its differential d: the space V is the union of an increasing...

1007/BFb0083797, ISBN 978-3-540-52468-7, MR 1052407. Nishida, Goro (1973), "The nilpotency of elements of the stable homotopy groups of spheres", Journal of the...

Soc. p. 332. ISBN 978-0-8218-4640-7. McCrimmon, Kevin (1983). "Strong nilpotence of solvable ideals in quadratic Jordan algebras" (PDF). Journal of Algebra...

problem in finite group theory which had stood for around sixty years: the nilpotency of Frobenius kernels. At the time, this achievement was noted in The New...