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

页码：399 / 417

页数：19

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