Add to ORKGWe study the coset covering function $\mathfrak{C}(r)$ of a finitely generated group: the number of cosets of infinite index subgroups needed to cover the ball of radius $r$. We show that $\mathfrak{C}(r)$ is of order at least $\sqrt{r}$ for all groups. Moreover, we show that $\mathfrak{C}(r)$ is linear for a class of amenable groups including virtually nilpotent and polycyclic groups, and that it is exponential for property (T) groups.Comment: 12 page
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We exhibit explicit infinite families of finitely presented, Kazhdan, simple groups that are pairwis...
We prove a quantitative refinement of the statement that groups of polynomial growth are finitely pr...
We say that a countable discrete group $\Gamma$ satisfies the invariant von Neumann subalgebras rigi...
International audienceWe study the coset covering function $C(r)$ of an infinite, finitely generated...
We study a family of finitely generated residually finite small cancellation groups. These groups ar...
Given an abstract group $G$, we study the function $ab_n(G) := \sup_{|G:H| \leq n} |H/[H,H]|$. If $G...
We show that for some absolute (explicit) constant C, the following holds for every finitely generat...
Let $F$ be a subfield of the algebraic closure of a finite field $\mathbb{F}_p$, $p \ne 2$, and let ...
The arithmetic regularity lemma due to Green [GAFA 2005] is an analogue of the famous Szemerédi regu...
Given a group G, we write x^G for the conjugacy class of G containing the element x. A famous theore...
Der Coset Poset ist die Menge aller Rechtsnebenklassen aller echten Untergruppen zusammen mit der Te...
We prove an inequality, valid on any finitely generated group with a fixed finite symmetric generati...
For a group $G$ acting on a set $X$, let $\text{End}_G(X)$ be the monoid of all $G$-equivariant tran...
A subset {g1, ..., gd} of a finite group G is said to invariably generate G if the set {g1x1,...,gdx...
We show that the finiteness length of an S-arithmetic subgroup Gamma in a noncommutative isotropic a...
We exhibit explicit infinite families of finitely presented, Kazhdan, simple groups that are pairwis...
We prove a quantitative refinement of the statement that groups of polynomial growth are finitely pr...
We say that a countable discrete group $\Gamma$ satisfies the invariant von Neumann subalgebras rigi...