Groups with Finitely Many Homomorphic Images of Finite Rank

被引：0

作者：

de Giovanni, Francesco ^{[1
]}

Russo, Alessio ^{[2
]}

机构：

[1] Univ Naples Federico II, Dipartimento Matemat & Applicaz, Complesso Univ Monte S Angelo,Via Cintia, I-L80126 Naples, Italy

[2] Univ Naples 2, Dipartimento Matemat & Fis, Via Lincoln 5, I-81100 Caserta, Italy

来源：

ALGEBRA COLLOQUIUM | 2016年 / 23卷 / 02期

关键词：

Prufer rank; Cernikov group; homomorphic image; SUBGROUPS;

D O I：

10.1142/S1005386716000201

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A group is called a Cernikov group if it is abelian-by-finite and satisfies the minimal condition on subgroups. A new characterization of Cernikov groups is given here, by proving that in a suitable large class of generalised soluble groups they coincide with the groups having only finitely many homomorphic images of finite rank (up to isomorphisms) and admitting an ascending normal series whose factors have finite rank.

引用

页码：181 / 187

页数：7

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