It is well-known that no knot can be cancelled in a connected sum with another knot, whereas every link up to link homotopy can be cancelled in a (componentwise) connected sum with another link. In this paper we address the question whether some form of the ‘complexity accumulation’ property of knots holds for (piecewiselinear) links up to some stronger analogue of link homotopy, which still do...

In this note we show that the nilpotence conjecture for toric varieties is true over any regular coefficient ring containing Q. In [G] we showed that for any additive submonoid M of a rational vector space with the trivial group of units and a field k with chark = 0 the multiplicative monoid N acts nilpotently on the quotient Ki(k[M ])/Ki(k) of the ith K-groups, i ≥ 0. In other words, for any s...

Let G denote a connected, quasi-split reductive group over a field F that is complete with respect to a discrete valuation and that has a perfect residue field. Under mild hypotheses, we produce a subset of the Lie algebra g(F ) that picks out a G(F )-conjugacy class in every stable, regular, topologically nilpotent conjugacy class in g(F ). This generalizes an earlier result obtained by DeBack...

the theorem 12 in [a note on $p$-nilpotence and solvability of finite groups, j. algebra 321(2009) 1555--1560.] investigated the non-abelian simple groups in which some maximal subgroups have primes indice. in this note we show that this result can be applied to prove that the finite groups in which every non-nilpotent maximal subgroup has prime index aresolvable.

Suppose that we are given a set S of powers of a prime p and that 1 ∈ S. A technique is presented that enables the construction of a p-group of specified nilpotence class n such that its set of irreducible character degrees is exactly S. If |S| ≥ 2, then this can be done for 2 ≤ n ≤ p and if p ∈ S, then the only requirement is 2 ≤ n.

Through an investigation of properties of Chern classes, Quillen discovered a connection between stable homotopy theory and 1-dimensional formal group laws [31]. After almost 40 years, the impacts of this connection are still being felt. The stratification of formal group laws in finite characteristic gives rise to the chromatic filtration in stable homotopy theory [32], and has definite calcul...

Contents Preface xi Introduction xiii 1 The main theorems 1 1.