WorldCat Identities

Grigorchuk, R. I.

Works: 9 works in 35 publications in 2 languages and 368 library holdings
Genres: Conference proceedings 
Roles: Editor, Thesis advisor, Author
Classifications: QA174, 512.2
Publication Timeline
Most widely held works by R. I Grigorchuk
Dynamical systems and group actions ( Book )
8 editions published in 2012 in English and held by 150 WorldCat member libraries worldwide
"This volume contains cutting-edge research from leading experts in ergodic theory, dynamical systems and group actions. A large part of the volume addresses various aspects of ergodic theory of general group actions including local entropy theory, universal minimal spaces, minimal models and rank one transformations. Other papers deal with interval exchange transformations, hyperbolic dynamics, transfer operators, amenable actions and group actions on graphs."--Page 4 of cover
Dynamical systems, automata, and infinite groups : collected papers by R. I Grigorchuk( Book )
6 editions published in 2000 in English and held by 12 WorldCat member libraries worldwide
Dinamičeskie sistemy, avtomaty i beskonečnye gruppy : sbornik statej ( Book )
5 editions published in 2000 in Russian and held by 5 WorldCat member libraries worldwide
Dinamicheskie sistemy, avtomaty i beskonechnye gruppy : sbornik stateĭ ( Book )
1 edition published in 2000 in Russian and held by 3 WorldCat member libraries worldwide
Solitons, geometry, and topology : on the crossroads ; collected papers dedicated to the 60th birthday of academician Sergei Petrovich Novikov ( Book )
1 edition published in 1999 in English and held by 1 WorldCat member library worldwide
Presentations and Structural Properties of Self-similar Groups and Groups without Free Sub-semigroups by Mustafa G Benli( )
1 edition published in 2013 in English and held by 1 WorldCat member library worldwide
This dissertation is devoted to the study of self-similar groups and related topics. It consists of three parts. The first part is devoted to the study of examples of finitely generated amenable groups for which every finitely presented cover contains non-abelian free subgroups. The study of these examples was motivated by natural questions about finiteness properties of finitely generated groups. We show that many examples of amenable self-similar groups studied in the literature cannot be covered by finitely presented amenable groups. We investigate the class of contracting self-similar groups from this perspective and formulate a general result which is used to detect this property. As an application we show that almost all known examples of groups of intermediate growth cannot be covered by finitely presented amenable groups. The latter is related to the problem of the existence of finitely presented groups of intermediate growth. The second part focuses on the study of one important example of a self-similar group called the first Grigorchuk group G, from the viewpoint of pro finite groups. We investigate finite quotients of this group related to presentations and group (co)homology. As an outcome of this investigation we prove that the pro finite completion G_hat of this group is not finitely presented as a pro finite group. The last part focuses on a class of recursive group presentations known as L-presentations, which appear in the study of self-similar groups. We investigate the relation of such presentations with the normal subgroup structure of finitely presented groups and show that normal subgroups with finite cyclic quotient of finitely presented groups have such presentations. We apply this result to finitely presented indicable groups without free sub-semigroups. The electronic version of this dissertation is accessible from
On Tychonoff groups by R. I Grigorchuk( Book )
1 edition published in 1995 in English and held by 0 WorldCat member libraries worldwide
Audience Level
Audience Level
  Kids General Special  
Audience level: 0.91 (from 0.00 for On Tychono ... to 1.00 for Dinamiches ...)
Alternative Names
Grigorchuk, Rostislav.
Grigorchuk, Rostislav Ivanovich
English (29)
Russian (6)