Nilpotence theorem information

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...

^{\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...

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...

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...

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

*-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...

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...

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...

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...

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...

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...

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}}}...

, {\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...

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...

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...

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...

group. Frobenius groups whose Fitting subgroup has arbitrarily large nilpotency class were constructed by Ito: Let q be a prime power, d a positive integer...

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...