On the autocommutator subgroup and absolute centre of a group

被引：9

作者：

Dietrich, Heiko ^{[1
]}

Moravec, Primoz ^{[2
]}

机构：

[1] Univ Auckland, Dept Math, Auckland, New Zealand

[2] Univ Ljubljana, Dept Math, Ljubljana, Slovenia

来源：

JOURNAL OF ALGEBRA | 2011年 / 341卷 / 01期

关键词：

Absolute centre; Autocommutator subgroup; Abelian groups; EXPONENTS; HOMOLOGY;

D O I：

10.1016/j.jalgebra.2011.05.038

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We show that if the quotient of a group by its absolute centre is locally finite of exponent n. then the exponent of its autocommutator subgroup is n-bounded, that is, bounded by a function depending only on n. If the group itself is locally finite, then its exponent is n-bounded as well. Under some extra assumptions, the exponent of its automorphism group is n-bounded. We determine the absolute centre and autocommutator subgroup for a large class of (infinite) abelian groups. (C) 2011 Elsevier Inc. All rights reserved.

引用

页码：150 / 157

页数：8

共 16 条

[1] VANKAMPEN THEOREMS FOR DIAGRAMS OF SPACES [J].