Groups with restrictions on subgroups of infinite rank

被引：27

作者：

De Falco, Maria ^{[1
]}

de Giovanni, Francesco ^{[1
]}

Musella, Carmela ^{[1
]}

Trabelsi, Nadir ^{[2
]}

机构：

[1] Univ Naples Federico II, Dipartimento Matemat & Applicaz, I-80126 Naples, Italy

[2] Univ Setif, Dept Math, Lab Fundamental & Numer Math, Setif 19000, Algeria

来源：

REVISTA MATEMATICA IBEROAMERICANA | 2014年 / 30卷 / 02期

关键词：

Prufer rank; strongly locally graded group; quasihamiltonian group; BY-FINITE GROUPS; CONJUGACY CLASSES; PROPER SUBGROUPS; LATTICE;

D O I：

10.4171/RMI/792

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

It is known that a (generalized) soluble group whose proper subgroups of infinite rank are abelian either is abelian or has finite rank. It is proved here that if G is a group of infinite rank such that all its proper subgroups of infinite rank have locally finite commutator subgroup, then the commutator subgroup G' of G is locally finite, provided that G satisfies a suitable generalized solubility condition. Moreover, a similar result is obtained for groups whose proper subgroups of infinite rank are quasihamiltonian.

引用

页码：537 / 550

页数：14