Related papers: Kazhdan groups have cost 1

We prove that the product of any two infinite countable groups has fixed price one. This resolves a longstanding problem posed by Gaboriau. The proof uses the propagation method to construct a Poisson horoball process as a weak limit of a…

We construct first examples of infinite groups having property (T) whose Kazhdan constants admit a lower bound independent of the choice of a finite generating set.

The main goal of this paper is to prove that every Golod-Shafarevich group has an infinite quotient with Kazhdan's property $(T)$. In particular, this gives an affirmative answer to the well-known question about non-amenability of…

For each countable group $Q$ we produce a short exact sequence $1\to N \to G \to Q\to 1$ where $G$ is f.g. and has a graphical $\frac16$ presentation and $N$ is f.g. and satisfies property $T$. As a consequence we produce a group $N$ with…

Kida and Tucker-Drob recently extended the notion of inner amenability from countable groups to discrete p.m.p. groupoids. In this article, we show that inner amenable groupoids have "fixed priced 1" in the sense that every principal…

Hutchcroft and Pete showed that countably infinite groups with Property (T) admit cost one actions, resolving a question of Gaboriau. We give a streamlined proof of their theorem, and extend it both to locally compact second countable…

We show that if $G$ is a non-archimedean, Roelcke precompact, Polish group, then $G$ has Kazhdan's property (T). Moreover, if $G$ has a smallest open subgroup of finite index, then $G$ has a finite Kazhdan set. Examples of such $G$ include…

We give bounds on Kazhdan constants of abelian extensions of (finite) groups. As a corollary, we improved known results of Kazhdan constants for some meta-abelian groups and for the relatively free group in the variety of $p$-groups of…

We prove that for every finitely generated group $\Gamma$, at least one of the following holds: (1) $\Gamma$ has fixed price; (2) each of its Cayley graphs $G$ has infinitely many infinite clusters for some Bernoulli percolation on $G$.

The main result of [4] is that all finitely presented groups of p-deficiency greater than one are p-large. Here we prove that groups with a finite presentation of p-deficiency one possess a finite index subgroup that surjects onto . This…

Let $G_1$ be a semisimple real Lie group and $G_2$ another locally compact second countable unimodular group. We prove that $G_1 \times G_2$ has fixed price one if $G_1$ has higher rank, or if $G_1$ has rank one and $G_2$ is a $p$-adic…

We prove that, for the free algebra over a sufficiently rich operad, a large subgroup of its group of tame automorphisms has Kazhdan's property (T). We deduce that there exists a group with property (T) that maps onto large powers of…

We construct the first examples of infinite sharply 2-transitive groups which are finitely generated. Moreover, we construct such a group that has Kazhdan property (T), is simple, has exactly four conjugacy classes, and we show that this…

D. A. Kahzdan first put forth property (T) in relation to the study of discrete subgroups of Lie groups of finite co-volume. Through a combinatorial approach, we define an analogue of property (T) for regular graphs. We then prove the basic…

In 2010, Invent. Math., Ershov and Jaikin-Zapirain proved Kazhdan's property (T) for elementary groups. This expository article focuses on presenting an alternative simpler proof of that. Unlike the original one, our proof supplies no…

We establish general criteria for a countable group $\Gamma$ to have fixed price 1 depending on a choice of left-invariant proper metric on $\Gamma$. We apply this criterion to show that if $\Gamma_1,\Gamma_2$ are two countable groups…

We give simple examples of Kazhdan groups with infinite outer automorphism groups. This answers a question of Paulin, independently answered by Ollivier and Wise by completely different methods. As arithmetic lattices in (non-semisimple)…

In 1993, Lubotzky and Weiss conjectured that if a compact group admits two finitely generated dense subgroups, one of which is amenable and the other has Kazhdan's property (T), then it would be finite. This conjecture was resolved in the…

It is shown that infinite, discrete, Kazhdan property (T) groups never have the {\it finite-dimensional density} (FDD) property. This answers a conjecture of Lubotzky and Shalom affirmatively.

We show that every finite group realizes as the outer automorphism group of an ICC hyperbolic group with Kazhdan property (T). This result complements the well-known theorem of Paulin stating that the outer automorphism group of every…