Groups with countably many subgroups

被引：3
|
作者：
Cutolo, Giovanni [1 ]
Smith, Howard [2 ]
机构：
[1] Univ Naples Federico II, Dipartimento Matemat & Applicaz R Caccioppoli, Via Cintia Monte S Angelo, I-80126 Naples, Italy
[2] Bucknell Univ, Dept Math, Lewisburg, PA 17837 USA
来源：
JOURNAL OF ALGEBRA | 2016年 / 448卷
关键词：
Soluble groups; Subgroups; Countable sets; Abelian subgroups; BY-FINITE GROUPS; RANK;
D O I：
10.1016/j.jalgebra.2015.10.007
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We describe soluble groups in which the set of all subgroups is countable and show that locally (soluble-by-finite) groups with this property are soluble-by-finite. Further, we construct a nilpotent group with uncountably many subgroups in which the set of all abelian subgroups is countable. (C) 2015 Elsevier Inc. All rights reserved.
引用
收藏
页码：399 / 417
页数：19
相关论文
共 50 条
  • [31] CARDINAL CHARACTERISTICS AND THE PRODUCT OF COUNTABLY MANY INFINITE CYCLIC GROUPS
    BLASS, A
    JOURNAL OF ALGEBRA, 1994, 169 (02) : 512 - 540
  • [32] GROUPS THAT ARE UNION OF FINITELY MANY PROPER SUBGROUPS
    SONN, J
    AMERICAN MATHEMATICAL MONTHLY, 1976, 83 (04): : 263 - 265
  • [33] Nondiscrete topological groups with many discrete subgroups
    Morris, SA
    Obraztsov, VN
    TOPOLOGY AND ITS APPLICATIONS, 1998, 84 (1-3) : 105 - 120
  • [34] Groups with many normal-by-finite subgroups
    Franciosi, S
    DeGiovanni, F
    PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1997, 125 (02) : 323 - 327
  • [35] On groups with many almost normal subgroups.
    Franciosi, S
    deGiovanni, F
    Kurdachenko, LA
    ANNALI DI MATEMATICA PURA ED APPLICATA, 1995, 169 : 35 - 65
  • [36] PERIODIC-GROUPS WITH MANY PERMUTABLE SUBGROUPS
    LONGOBARDI, P
    MAJ, M
    RHEMTULLA, A
    SMITH, H
    JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY SERIES A-PURE MATHEMATICS AND STATISTICS, 1992, 53 : 116 - 119
  • [37] Groups with infinitely many types of fixed subgroups
    Hsu, T
    Wise, DT
    ISRAEL JOURNAL OF MATHEMATICS, 2004, 144 (1) : 93 - 107
  • [38] Groups with many self-normalizing subgroups
    De Falco, M.
    de Giovanni, F.
    Musella, C.
    ALGEBRA & DISCRETE MATHEMATICS, 2009, (04): : 55 - 65
  • [39] A generalization of groups with many almost normal subgroups
    Russo, Francesco G.
    ALGEBRA & DISCRETE MATHEMATICS, 2010, 9 (01): : 79 - 85
  • [40] Solvable groups with many BFC-subgroups
    Artemovych, OD
    PUBLICACIONS MATEMATIQUES, 2000, 44 (02) : 491 - 501
12345