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.
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页码：399 / 417
页数：19
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