Verbal width in anabelian groups

On the verbal width of finitely generated pro-p groups

Let p be a prime. It is proved that a non-trivial word w from a free group F has finite width in every finitely generated pro-p group if and only if w 6∈ (F ′)pF ′′. Also it is shown that any word w has finite width in a compact p-adic group.

Verbal subgroups of hyperbolic groups have infinite width

Topics in Absolute Anabelian Geometry Ii: Decomposition Groups and Endomorphisms

The present paper, which forms the second part of a three-part series in which we study absolute anabelian geometry from an algorithmic point of view, focuses on the study of the closely related notions of decomposition groups and endomorphisms in this anabelian context. We begin by studying an abstract combinatorial analogue of the algebro-geometric notion of a stable polycurve [i.e., a “succe...

Verbal Synchrony in Large Groups

Metronomes, cells, neurons, fireflies, and human beings all fall into synchrony with each other, given the opportunity. Synchrony between people appears to generate social cohesion by increasing liking and feelings of togetherness. But the function of dancing, chanting and singing is not just to produce warm, affiliative feelings, anthropologists have speculated, but also to improve group actio...

the verbal constructions in azari (harzani dialect)

most of the verbal constructions of harzani dialect have got inflectional affixes. the majority of the constructions are made up vy adding a specific verbal affix to the verbal stem (infinitive without infinitive marker). only a few number of them is formed by adding a verbal affix to the past participle of the verb. there are specific rules for the formation of different verbal types. there is...