Certain Locally Nilpotent Varieties of Groups

Dominions in varieties of nilpotent groups

The concept of dominion (in the sense of Isbell) is investigated in several varieties of nilpotent groups. A complete description of dominions in the variety of nilpotent groups of class at most 2 is given, and used to prove nontriviality of dominions in the variety of nilpotent groups of class at most c for any c>1 . Some subvarieties of N2 , and the variety of all nilpotent groups of class at...

Literal Varieties of Languages Induced by Homomorphisms onto Nilpotent Groups

We present here new hierarchies of literal varieties of languages. Each language under consideration is a disjoint union of a certain collection of “basic” languages described here. Our classes of languages correspond to certain literal varieties of homomorphisms from free monoids onto nilpotent groups of class ≤ 2.

Finite Groups With a Certain Number of Elements Pairwise Generating a Non-Nilpotent Subgroup

Subgroups defining automorphisms in locally nilpotent groups

We investigate some situation in which automorphisms of a groupG are uniquely determined by their restrictions to a proper subgroup H . Much of the paper is devoted to studying under which additional hypotheses this property forces G to be nilpotent if H is. As an application we prove that certain countably infinite locally nilpotent groups have uncountably many (outer) automorphisms.

Representation Zeta Functions of Some Nilpotent Groups Associated to Prehomogenous Vector Spaces

We compute the representation zeta functions of some finitely generated nilpotent groups associated to unipotent group schemes over rings of integers in number fields. These group schemes are defined by Lie lattices whose presentations are modelled on certain prehomogeneous vector spaces. Our method is based on evaluating p-adic integrals associated to certain rank varieties of linear forms.