The acyclic group dichotomy

被引：3
作者：
Berrick, A. J. [1 ]
机构：
[1] Natl Univ Singapore, Dept Math, Kent Ridge 119076, Singapore
来源：
JOURNAL OF ALGEBRA | 2011年 / 326卷 / 01期
关键词：
Acyclic group; Bass conjecture; Baum-Connes conjecture; Binate group; Cohomological dimension; Farkas conjecture; Frattini embedding; Hattori-Stallings trace; Perfect group; COHOMOLOGICAL DIMENSION; CLASSIFYING SPACE; K-THEORY; CONJECTURE; HOMOLOGY; PERFECT;
D O I：
10.1016/j.jalgebra.2010.05.009
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Two extremal classes of acyclic groups are discussed. For an arbitrary group G, there is always a homomorphism from an acyclic group of cohomological dimension 2 onto the maximum perfect subgroup of G, and there is always an embedding of G in a binate (hence acyclic) group. In the other direction, there are no nontrivial homomorphisms from binate groups to groups of finite cohomological dimension. Binate groups are shown to be of significance in relation to a number of important K-theoretic isomorphism conjectures. (C) 2010 Elsevier Inc. All rights reserved.
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页码：47 / 58
页数：12
相关论文
共 35 条
  • [11] Acyclic groups and wild arcs
    Berrick, AJ
    Wong, YL
    [J]. QUARTERLY JOURNAL OF MATHEMATICS, 2004, 55 : 421 - 440
  • [12] BINATE TOWERS OF GROUPS
    BERRICK, AJ
    VARADARAJAN, K
    [J]. ARCHIV DER MATHEMATIK, 1994, 62 (02) : 97 - 111
  • [13] From acyclic groups to the Bass conjecture for amenable groups
    Berrick, AJ
    Chatterji, I
    Mislin, G
    [J]. MATHEMATISCHE ANNALEN, 2004, 329 (04) : 597 - 621
  • [14] Perfect and acyclic subgroups of finitely presentable groups
    Berrick, AJ
    Hillman, JA
    [J]. JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES, 2003, 68 : 683 - 698
  • [15] BERRICK AJ, 2002, OXFORD GRADUATE TEXT, V5, P1
  • [16] BERRICK AJ, TOPOLOGICAL HOCHSCHI
  • [17] BERRICK AJ, 2007, GEOM TOPOL MONOGR, V10, P41
  • [18] CHATTERJI I, 2003, ENSEIGN MATH, V49
  • [19] DELAHARPE P, 1983, COMMENT MATH HELV, V58, P48
  • [20] Cohomological dimension with respect to perfect groups
    Dranishnikov, Alexander N.
    Repovs, Dusan
    [J]. TOPOLOGY AND ITS APPLICATIONS, 1996, 74 (1-3) : 123 - 140
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