Polynomial structures for nilpotent groups

Polynomial Structures for Nilpotent Groups

If a polycyclic-by-finite rank-K group Γ admits a faithful affine representation making it acting on RK properly discontinuously and with compact quotient, we say that Γ admits an affine structure. In 1977, John Milnor questioned the existence of affine structures for such groups Γ. Very recently examples have been obtained showing that, even for torsion-free, finitely generated nilpotent group...

Topological multiple recurrence for polynomial configurations in nilpotent groups

We establish a general multiple recurrence theorem for an action of a nilpotent group by homeomorphisms of a compact space. This theorem can be viewed as a nilpotent version of our recent polynomial Hales-Jewett theorem ([BL2]) and contains nilpotent extensions of many known “abelian” results as special cases. 0. Introduction 0.1. The celebrated van der Waerden theorem on arithmetic progression...

Nilpotent Elements in Skew Polynomial Rings

 Letbe a ring with an endomorphism and an -derivationAntoine studied the structure of the set of nilpotent elements in Armendariz rings and introduced nil-Armendariz rings. In this paper we introduce and investigate the notion of nil--compatible rings. The class of nil--compatible rings are extended through various ring extensions and many classes of nil--compatible rings are constructed. We al...

Nilpotent Groups

The articles [2], [3], [4], [6], [7], [5], [8], [9], [10], and [1] provide the notation and terminology for this paper. For simplicity, we use the following convention: x is a set, G is a group, A, B, H, H1, H2 are subgroups of G, a, b, c are elements of G, F is a finite sequence of elements of the carrier of G, and i, j are elements of N. One can prove the following propositions: (1) ab = a · ...

Some Inequalities for Nilpotent Multipliers of Powerful p-Groups