Let G be a finite 2-group of maximal nilpotency class, and let BG be its classifying space. We prove that iterated Massey products inH∗(BG;F2) do characterize the homotopy type of BG among 2-complete spaces with the same cohomological structure. As a consequence we get an alternative proof of the modular isomorphism problem for 2-groups of maximal nilpotency class.

Nilpotency of the pure spinor BRST operator in a curved background implies superspace equations of motion for the background. By computing one-loop corrections to nilpotency for the heterotic sigma model, the Yang-Mills Chern-Simons corrections to the background are derived.

It is known that strongly nilpotent matrices over a division ring are linearly triangularizable. We describe the structure of such matrices in terms of the strong nilpotency index. We apply our results on quasi-translation x+H such that JH has strong nilpotency index two.

We describe algorithms for testing polycyclicity and nilpotency for finitely generated subgroups of GL(d,Q) and thus we show that these properties are decidable. Variations of our algorithm can be used for testing virtual polycyclicity and virtual nilpotency for finitely generated subgroups of GL(d,Q).

Given a sequence d→=(d1,…,dk) of natural numbers, we consider the Lie subalgebra h gl(d,F), where d=d1+⋯+dk and F is field characteristic 0, generated by two block upper triangular matrices D E partitioned according to d→, study problem computing nilpotency degree m nilradical n h. We obtain complete answer when belong certain family that arises naturally attempting classify indecomposable modu...

A discrete (finite-difference) analogue of differential forms is considered, defined on simplicial complexes, including triangulations of continuous manifolds. Various operations are explicitly defined on these forms, including exterior derivative and exterior product. The latter one is non-associative. Instead, as anticipated, it is a part of non-trivial A ∞ structure, involving a chain of pol...

Abstract Let G be a finite group and assume that of automorphisms A acts on , such the orders are relatively prime. We prove fact imposing certain conditions set maximal -invariant subgroups relating to nilpotency, p -nilpotency, normality or having p’ -order, determines properties structure as solubility, -solubility -nilpotency.

It is known that a right nilpotent congruence on a-nite algebra A is also left nilpotent Kea93]. The question on whether the left nilpotency class of is less than or equal to the right nilpo-tency class of is still open. In this paper we nd an upper limit for the left nilpotency class of. In addition, under the assumption that 1 6 2 typ fAg, we show that (] k =) k for all k 1. Thus the left and...