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2012, Contemporary mathematics, ISBN 0821869221, Volume 567., xi, 264
Book
Proceedings of the Steklov Institute of Mathematics, ISSN 0081-5438, 7/2011, Volume 273, Issue 1, pp. 64 - 175
This article combines the features of a survey and a research paper. It presents a review of some results obtained during the last decade in problems related... 
Mathematics, general | Mathematics | HAUSDORFF DIMENSION | MATHEMATICS | MATHEMATICS, APPLIED | ALGEBRAS | TOWERS | SCHREIER GRAPHS | RANDOM-WALKS | AMENABILITY | AMENABLE GROUP | AUTOMATON | CONJUGACY PROBLEM | EQUIVALENCE-RELATIONS
Journal Article
Sbornik Mathematics, ISSN 1064-5616, 2014, Volume 205, Issue 6, pp. 843 - 861
We discuss the algebraic structure of the topological full group [[T]] of a Cantor minimal system (X, T). We show that [[T]] has a structure similar to a union... 
Full group | Finitely generated group | Cantor system | Amenable group | Simple group | MATHEMATICS | simple group | HOMEOMORPHISMS | RECONSTRUCTION | CANTOR SYSTEMS | finitely generated group | amenable group | full group | ORBIT EQUIVALENCE | Embedded systems | Algebra | Mathematical analysis | Topology | Commutators | Invariants | Subgroups | Unions
Journal Article
European Journal of Combinatorics, ISSN 0195-6698, 10/2012, Volume 33, Issue 7, pp. 1574 - 1587
We study the relation between the diameter, the first positive eigenvalue of the discrete -Laplacian, and the -distortion of a finite graph. We prove an... 
MATHEMATICS | P-LAPLACIAN | TOWERS | AUTOMATON | SPECTRUM | GRAPHS | Approximation | Mathematical analysis | Eigenvalues | Distortion | Graphs | Spectra | Combinatorial analysis | Convergence
Journal Article
Geometriae Dedicata, ISSN 0046-5755, 8/2001, Volume 87, Issue 1, pp. 209 - 244
We realize the lamplighter group $$\mathbb{Z}$$ /2 $$\mathbb{Z}$$ ≀ $$\mathbb{Z}$$ as a group defined by a 2-state automaton. We study the corresponding action... 
Geometry | random walks | Mathematics | Følner sets | automata groups | spectral measure | Automata groups | Spectral measure | Random walks | MATHEMATICS | RANDOM-WALKS | GROWTH | Folner sets
Journal Article
RUSSIAN MATHEMATICAL SURVEYS, ISSN 0036-0279, 2016, Volume 71, Issue 4, pp. 793 - 800
In 2015 the prominent mathematician and leading expert in modern algebra Efim Isaakovich Zelmanov observed his 60th birthday. 
LIE-ALGEBRAS | MATHEMATICS | JORDAN SUPERALGEBRAS | REPRESENTATIONS | Mathematical analysis | Algebra
Journal Article
Geometric and Functional Analysis, ISSN 1016-443X, 03/2009, Volume 18, Issue 6, pp. 1841 - 1874
We introduce two new types of Dehn functions of group presentations which seem more suitable (than the standard Dehn function) for infinite group presentations... 
torsion groups | Burnside groups | Presentation of groups | Analysis | word problem | Mathematics | Dehn functions | van Kampen diagrams | Primary 20E08, 20F05, 20F06, 20F10, 20F50, 20F65, 20F69 | Van Kampen diagrams | Word problem | Torsion groups | MATHEMATICS | PRODUCTS | COMPLEXITY | Universities and colleges
Journal Article
RUSSIAN MATHEMATICAL SURVEYS, ISSN 0036-0279, 2015, Volume 70, Issue 2, pp. 369 - 381
Journal Article
International Journal of Algebra and Computation, ISSN 0218-1967, 2002, Volume 12, Issue 1-2, pp. 223 - 246
We study a torsion free weakly branch group G without free subgroups defined by a three state automaton which appears in different problems related to... 
MATHEMATICS | Robots
Journal Article
Journal of the London Mathematical Society, ISSN 0024-6107, 12/2003, Volume 68, Issue 3, pp. 671 - 682
Further properties of a group Γ introduced by the first author in 1980 (sometimes called the first Grigorchuk group) are established. These are notably that... 
MATHEMATICS
Journal Article
Geometriae Dedicata, ISSN 0046-5755, 8/2003, Volume 100, Issue 1, pp. 103 - 116
It is proved that in many cases of interest the actions of groups on rooted trees can be recovered from the structure of the groups. The results apply to most... 
Geometry | vertex subgroups | Mathematics | basal subgroups | rooted trees | group actions | Basal subgroups | Vertex subgroups | Rooted trees | Group actions | MATHEMATICS | FINITE | SUBGROUPS
Journal Article
INTERNATIONAL JOURNAL OF ALGEBRA AND COMPUTATION, ISSN 0218-1967, 12/2004, Volume 14, Issue 5-6, pp. 667 - 676
The automorphism group of a 3-generated 2-group G of intermediate growth is determined and it is shown that the outer group of automorphisms of G is an... 
MATHEMATICS | burnside groups | automorphisms of groups | BRANCH GROUPS | ROOTED TREES | just-infinite groups | intermediate growth | Burnside groups | Just-infinite groups | Intermediate growth | Automorphisms of groups
Journal Article
Theoretical Computer Science, ISSN 0304-3975, 1999, Volume 215, Issue 1, pp. 325 - 327
We give an example of a language belonging to the class of indexed languages whose growth is intermediate. In particular, the growth function of this language... 
COMPUTER SCIENCE, THEORY & METHODS
Journal Article
Mathematical Notes, ISSN 0001-4346, 5/1999, Volume 65, Issue 5, pp. 654 - 657
Journal Article
Mathematical Notes, ISSN 0001-4346, 6/2000, Volume 67, Issue 6, pp. 718 - 723
The class of branch groups is defined (both in the abstract and in the profinite category). The relationship of this class with the class of extremal groups is... 
congruence property | parabolic subgroup | weakly maximal subgroup | Mathematics, general | Mathematics | profinite group | branch group | extremal group | Profinite group | Branch group | Parabolic subgroup | Weakly maximal subgroup | Congruence property | Extremal group | MATHEMATICS
Journal Article
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