Embeddings in finitely presented groups which preserve the center

被引：10

作者：

Houcine, Abderezak Ould ^{[1
]}

机构：

[1] Univ Lyon 1, F-69622 Villeurbanne, France

来源：

JOURNAL OF ALGEBRA | 2007年 / 307卷 / 01期

关键词：

finitely presented groups; center of finitely presented groups; abelian groups;

D O I：

10.1016/j.jalgebra.2006.07.015

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

V.N. Remeslennikov proposed in 1976 the following problem: is any countable abelian group a subgroup of the center of some finitely presented group? We prove that every finitely generated recursively presented group G is embeddable in a finitely presented group K such that the center of G coincide with that of K. We prove also that there exists a finitely presented group H with soluble word problem such that every countable abelian group is embeddable in the center of H. This gives a strong positive answer to the question raised by V.N. Remeslennikov. (C) 2006 Elsevier Inc. All rights reserved.

引用

页码：1 / 23

页数：23