ﻻ يوجد ملخص باللغة العربية
Let $G$ be a virtually special group. Then the residual finiteness growth of $G$ is at most linear. This result cannot be found by embedding $G$ into a special linear group. Indeed, the special linear group $text{SL}_k(mathbb{Z})$, for $k > 2$, has residual finiteness growth $n^{k-1}$.
Full residual finiteness growth of a finitely generated group $G$ measures how efficiently word metric $n$-balls of $G$ inject into finite quotients of $G$. We initiate a study of this growth over the class of nilpotent groups. When the last term of
We show that many 2-dimensional Artin groups are residually finite. This includes 3-generator Artin groups with labels $geq$ 3 where either at least one label is even, or at most one label is equal 3. As a first step towards residual finiteness we sh
We give a conjectural classification of virtually cocompactly cubulated Artin-Tits groups (i.e. having a finite index subgroup acting geometrically on a CAT(0) cube complex), which we prove for all Artin-Tits groups of spherical type, FC type or two-
We prove that any word hyperbolic group which is virtually compact special (in the sense of Haglund and Wise) is conjugacy separable. As a consequence we deduce that all word hyperbolic Coxeter groups and many classical small cancellation groups are
A function $mathbb{N} to mathbb{N}$ is near exponential if it is bounded above and below by functions of the form $2^{n^c}$ for some $c > 0$. In this article we develop tools to recognize the near exponential residual finiteness growth in groups acti