COSET ENUMERATION FOR CERTAIN INFINITELY PRESENTED GROUPS

被引：6
作者：
Hartung, Rene [1 ]
机构：
[1] Univ Gottingen, Math Inst, D-37073 Gottingen, Germany
来源：
INTERNATIONAL JOURNAL OF ALGEBRA AND COMPUTATION | 2011年 / 21卷 / 08期
关键词：
Coset enumeration; recursive presentations; self-similar groups; Grigorchuk group; low-index subgroups; SUBGROUPS;
D O I：
10.1142/S0218196711006637
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We describe an algorithm that computes the index of a finitely generated subgroup in a finitely L-presented group provided that this index is finite. This algorithm shows that the subgroup membership problem for finite index subgroups in a finitely L-presented group is decidable. As an application, we consider the low-index subgroups of some self-similar groups including the Grigorchuk group, the twisted twin of the Grigorchuk group, the Grigorchuk super-group, and the Hanoi 3-group.
引用
收藏
页码：1369 / 1380
页数：12
相关论文
共 28 条
  • [1] [Anonymous], 1994, ENCY MATH ITS APPL
  • [2] Amenability via random walks
    Bartholdi, L
    Virág, B
    [J]. DUKE MATHEMATICAL JOURNAL, 2005, 130 (01) : 39 - 56
  • [3] Lie algebras and growth in branch groups
    Bartholdi, L
    [J]. PACIFIC JOURNAL OF MATHEMATICS, 2005, 218 (02) : 241 - 282
  • [4] Endomorphic presentations of branch groups
    Bartholdi, L
    [J]. JOURNAL OF ALGEBRA, 2003, 268 (02) : 419 - 443
  • [5] Bartholdi L., 2002, Serdica Math. J., V28, P47
  • [6] Bartholdi L., 2003, Handbook of algebra, V3, P989
  • [7] THE TWISTED TWIN OF THE GRIGORCHUK GROUP
    Bartholdi, Laurent
    Siegenthaler, Olivier
    [J]. INTERNATIONAL JOURNAL OF ALGEBRA AND COMPUTATION, 2010, 20 (04) : 465 - 488
  • [8] A NILPOTENT QUOTIENT ALGORITHM FOR CERTAIN INFINITELY PRESENTED GROUPS AND ITS APPLICATIONS
    Bartholdi, Laurent
    Eick, Bettina
    Hartung, Rene
    [J]. INTERNATIONAL JOURNAL OF ALGEBRA AND COMPUTATION, 2008, 18 (08) : 1321 - 1344
  • [9] Baumslag Gilbert., 1971, Bull. Austral. Math. Soc, V5, P131
  • [10] DETERMINING SUBGROUPS OF A GIVEN FINITE INDEX IN A FINITELY PRESENTED GROUP
    DIETZE, A
    SCHAPS, M
    [J]. CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES, 1974, 26 (04): : 769 - 782
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