40 citations · 226 across the 15 of their papers we have counts for
16 papers
On groups that can be covered by conjugates of finitely many cyclic or procyclic subgroups
Yiftach Barnea, Rachel Camina, Mikhail Ershov +1
Given a discrete (resp. profinite) group , we define to be the smallest number of cyclic (resp. procyclic) subgroups of whose conjugates cover . In this paper we…
On the second cohomology of the norm one group of a p-adic division algebra
Mikhail Ershov, Thomas Weigel
Let be a -adic field, that is, a finite extension of . Let be a finite-dimensional central division algebra over and let be the group of eleme…
Effective finite generation for [IA_n,IA_n] and the Johnson kernel
Mikhail Ershov, Daniel Franz
Let denote the group of -automorphisms of a free group of rank , and let denote the Torelli subgroup of the mapping class group of an orientable surf…
On finite generation of the Johnson filtrations
Thomas Church, Mikhail Ershov, Andrew Putman
We prove that every term of the lower central series and Johnson filtrations of the Torelli subgroups of the mapping class group and the automorphism group of a free group is finit…
Property (T) for Kac-Moody groups over rings
Mikhail Ershov, Ashley Rall, Zezhou Zhang
Let R be a finitely generated commutative ring with 1, let A be an indecomposable 2-spherical generalized Cartan matrix of size at least 2 and M=M(A) the largest absolute value of…
On finiteness properties of the Johnson filtrations
Mikhail Ershov, Sue He
Let A denote either the automorphism group of the free group of rank n>=4 or the mapping class group of an orientable surface of genus n>=12 with at most 1 boundary component, and…
The Tarski numbers of groups
Mikhail Ershov, Gili Golan, Mark Sapir
The Tarski number of a non-amenable group G is the minimal number of pieces in a paradoxical decomposition of G. In this paper we investigate how Tarski numbers may change under va…
Golod-Shafarevich groups: a survey
Mikhail Ershov
In this paper we survey the main results about Golod-Shafarevich groups and their applications in algebra, number theory and topology.
The first -Betti number and approximation in arbitrary characteristic
Mikhail Ershov, Wolfgang Lueck
Let G be a finitely generated group and (G_i) a descending chain of finite index normal subgroups of G. Given a field K, we consider the sequence b_1(G_i;K)/[G:G_i] of normalized f…
Property (T) for groups graded by root systems
Mikhail Ershov, Andrei Jaikin-Zapirain, Martin Kassabov
We introduce and study the class of groups graded by root systems. We prove that if Φ is an irreducible classical root system of rank at least 2 and G is a group graded by Φ, then…
Groups of positive weighted deficiency and their applications
Mikhail Ershov, Andrei Jaikin-Zapirain
In this paper we introduce the concept of weighted deficiency for abstract and pro- groups and study groups of positive weighted deficiency which generalize Golod-Shafarevich gr…
The congruence subgroup property for : A group-theoretic proof of Asada's theorem
Kai-Uwe Bux, Mikhail Ershov, Andrei Rapinchuk
The goal of this paper is to give a group-theoretic proof of the congruence subgroup property for , the group of automorphisms of a free group on two generators. This res…
Kazhdan quotients of Golod-Shafarevich groups
Mikhail Ershov, Andrei Jaikin-Zapirain
The main goal of this paper is to prove that every Golod-Shafarevich group has an infinite quotient with Kazhdan's property . In particular, this gives an affirmative answer t…
Abstract commensurators of profinite groups
Yiftach Barnea, Mikhail Ershov, Thomas Weigel
In this paper we initiate a systematic study of the abstract commensurators of profinite groups. The abstract commensurator of a profinite group is a group which depe…
Property for noncommutative universal lattices
Mikhail Ershov, Andrei Jaikin-Zapirain
We establish a new spectral criterion for Kazhdan's property which is applicable to a large class of discrete groups defined by generators and relations. As the main applicat…
Abstract simplicity of complete Kac-Moody groups over finite fields
Lisa Carbone, Mikhail Ershov, Gordon Ritter
Let be a Kac-Moody group over a finite field corresponding to a generalized Cartan matrix , as constructed by Tits. It is known that admits the structure of a BN-pair, a…