ON THE UPPER CENTRAL SERIES OF INFINITE GROUPS

被引：27

作者：

De Falco, M. ^{[1
]}

de Giovanni, F. ^{[1
]}

Musella, C. ^{[1
]}

Sysak, Y. P. ^{[2
]}

机构：

[1] Univ Naples Federico 2, Dipartimento Matemat & Applicaz, I-80126 Naples, Italy

[2] Natl Acad Sci Ukraine, Inst Math, UA-01601 Kiev, Ukraine

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2011年 / 139卷 / 02期

关键词：

Upper central series; hypercentre; hypercentral group;

D O I：

10.1090/S0002-9939-2010-10625-1

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Two relevant theorems by R. Baer and P. Hall show that a group is finite over a term with finite ordinal type of its upper central series if and only if it is finite-by-nilpotent. Extending these results, we prove here that if G is any group, the hypercentre factor group G/(Z) over bar (G) is finite if and only if G contains a finite normal subgroup N such that G/N is hypercentral (where the hypercentre Z(G) of G is defined as the last term of its upper central series).

引用

页码：385 / 389

页数：5