Mikhail Ershov
Groups of positive weighted deficiency and their applications.
Mon, 07/12/2010 - 15:01 — SomNambulAuthors: Mikhail Ershov, Andrei Jaikin-Zapirain
Subjects: Group Theory
AbstractIn this paper we introduce the concept of weighted deficiency for abstract
and pro-$p$ groups and study groups of positive weighted deficiency which
generalize Golod-Shafarevich groups. In order to study weighted deficiency we
introduce weighted versions of the notions of rank for groups and index for
subgroups and establish weighted analogues of several classical results in
combinatorial group theory, including the Schreier index formula. Two main
applications of groups of positive weighted deficiency are given.The congruence subgroup property for $Aut F_2$: A group-theoretic proof of Asada's theorem.
Thu, 09/03/2009 - 17:38 — SomNambulAuthors: Mikhail Ershov, Kai-Uwe Bux, Andrei Rapinchuk
Subjects: Group Theory
AbstractThe goal of this paper is to give a group-theoretic proof of the congruence
subgroup property for $Aut(F_2)$, the group of automorphisms of a free group on
two generators. This result was first proved by Asada using techniques from
anabelian geometry, and our proof is, to a large extent, a translation of
Asada's proof into group-theoretic language. This translation enables us to
simplify many parts of Asada's original argument and prove a quantitative
version of the congruence subgroup property for $Aut(F_2)$.Kazhdan quotients of Golod-Shafarevich groups.
Thu, 08/27/2009 - 13:23 — SomNambulAuthors: Mikhail Ershov, Andrei Jaikin-Zapirain
Subjects: Group Theory
AbstractThe 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
Golod-Shafarevich groups.
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