On torsion-free minimal abelian groups

被引：2
|
作者：
OhOgáin, S [1 ]
机构：
[1] Dublin Inst Technol, Sch Math Sci, Dublin 12, Ireland
来源：
COMMUNICATIONS IN ALGEBRA | 2005年 / 33卷 / 07期
关键词：
D O I：
10.1081/AGB-200063605
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
An abelian group is said to he minimal if it is isomorphic to all its subgroups of finite index. In this article we show that torsion-free groups which are complete in their Z-adic topology or are of p-rank not greater than 1, for all primes p, are minimal. A criterion is found for the minimality of all finite rank and for large classes of infinite rank completely decomposable groups. Separable minimal groups are also considered.
引用
收藏
页码：2339 / 2350
页数：12
相关论文
共 50 条
  • [31] COBALANCED TORSION-FREE ABELIAN-GROUPS
    GOETERS, HP
    COMMUNICATIONS IN ALGEBRA, 1993, 21 (08) : 2715 - 2726
  • [32] ON TORSION-FREE ABELIAN K-GROUPS
    DUGAS, M
    RANGASWAMY, KM
    PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1987, 99 (03) : 403 - 408
  • [33] Direct Decompositions of Torsion-Free Abelian Groups
    E. Blagoveshchenskaya
    Lobachevskii Journal of Mathematics, 2020, 41 : 1640 - 1646
  • [34] JUMP DEGREES OF TORSION-FREE ABELIAN GROUPS
    Andersen, Brooke M.
    Kach, Asher M.
    Melnikov, Alexander G.
    Solomon, Reed
    JOURNAL OF SYMBOLIC LOGIC, 2012, 77 (04) : 1067 - 1100
  • [35] ABELIAN TORSION-FREE GROUPS WITH PERIODIC-GROUPS OF AMORPHISMS
    BEKKER, IK
    IZVESTIYA VYSSHIKH UCHEBNYKH ZAVEDENII MATEMATIKA, 1986, (02): : 3 - 12
  • [36] Multiplication Groups of Abelian Torsion-Free Groups of Finite Rank
    Kompantseva, E. I.
    Tuganbaev, A. A.
    MEDITERRANEAN JOURNAL OF MATHEMATICS, 2023, 20 (04)
  • [37] Multiplication Groups of Abelian Torsion-Free Groups of Finite Rank
    E. I. Kompantseva
    A. A. Tuganbaev
    Mediterranean Journal of Mathematics, 2023, 20
  • [38] QUASIPURE INJECTIVE TORSION-FREE ABELIAN-GROUPS
    CHEKHLOV, AR
    MATHEMATICAL NOTES, 1989, 46 (3-4) : 739 - 743
  • [39] 3 EXAMPLES ON HOPFICITY IN TORSION-FREE ABELIAN GROUPS
    CORNER, ALS
    ACTA MATHEMATICA ACADEMIAE SCIENTIARUM HUNGARICAE, 1965, 16 (3-4): : 303 - &
  • [40] Decidability and Computability of Certain Torsion-Free Abelian Groups
    Downey, Rodney G.
    Goncharov, Sergei S.
    Kach, Asher M.
    Knight, Julia F.
    Kudinov, Oleg V.
    Melnikov, Alexander G.
    Turetsky, Daniel
    NOTRE DAME JOURNAL OF FORMAL LOGIC, 2010, 51 (01) : 85 - 96
12345