A minimal Cantor set in the space of 3-generated groups

被引：23
|
作者：
Nekrashevych, Volodymyr [1 ]
机构：
[1] Texas A&M Univ, Dept Math, College Stn, TX 77843 USA
来源：
GEOMETRIAE DEDICATA | 2007年 / 124卷 / 01期
关键词：
space of groups; self-Similar groups; iterated monodromy groups;
D O I：
10.1007/s10711-006-9118-4
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We construct and study a family of 3-generated groups D-w parametrized by infinite binary sequences w. We show that two groups of the family are isomorphic if and only if the sequences are cofinal and that two groups cannot be distinguished by finite sets of relations. We show a connection of the family with 2-dimensional holomorphic dynamics.
引用
收藏
页码：153 / 190
页数：38
相关论文
共 50 条
  • [1] A minimal Cantor set in the space of 3-generated groups
    Volodymyr Nekrashevych
    Geometriae Dedicata, 2007, 124 : 153 - 190
  • [2] Minimal 3-generated Majorana algebras
    Mamontov, Andrey
    Staroletov, Alexey
    Whybrow, Madeleine
    JOURNAL OF ALGEBRA, 2019, 524 : 367 - 394
  • [3] On finite 3-generated 2-groups of Alperin
    Veretennikov, B. M.
    SIBERIAN ELECTRONIC MATHEMATICAL REPORTS-SIBIRSKIE ELEKTRONNYE MATEMATICHESKIE IZVESTIYA, 2007, 4 : 155 - 168
  • [4] AN UNCOUNTABLE FAMILY OF 3-GENERATED GROUPS WITH ISOMORPHIC PROFINITE COMPLETIONS
    Nekrashevych, Volodymyr
    INTERNATIONAL JOURNAL OF ALGEBRA AND COMPUTATION, 2014, 24 (01) : 33 - 46
  • [5] THE GROUPS OF TWO CLASSES OF CERTAIN CYCLICALLY PRESENTED GROUPS ARE ESSENTIALLY 3-GENERATED
    Stoddart, Devon Roy
    ITALIAN JOURNAL OF PURE AND APPLIED MATHEMATICS, 2012, (29): : 395 - 402
  • [6] ON 3-GENERATED 2-GROUPS WHOSE MAXIMAL SUBGROUPS ARE 2-GENERATED
    Crestani, Eleonora
    COMMUNICATIONS IN ALGEBRA, 2011, 39 (03) : 881 - 887
  • [7] Full groups of Cantor minimal systems
    Giordano, T
    Putnam, IF
    Skau, CF
    ISRAEL JOURNAL OF MATHEMATICS, 1999, 111 (1) : 285 - 320
  • [8] Full groups of Cantor minimal systems
    Thierry Giordano
    Ian F. Putnam
    Christian F. Skau
    Israel Journal of Mathematics, 1999, 111 : 285 - 320
  • [9] 3-Generated Lattices Close to Distributive Ones
    Gein, A. G.
    Maslintsyn, I. D.
    Maslintsyna, K. E.
    Selivanov, K. V.
    ALGEBRA AND LOGIC, 2023, 62 (04) : 339 - 352
  • [10] FINITE SUBLATTICES OF 3-GENERATED LATTICES
    DAVEY, BA
    RIVAL, I
    NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY, 1974, 21 (05): : A484 - A484
12345