ABSTRACT COMMENSURATORS OF SOLVABLE BAUMSLAG-SOLITAR GROUPS

被引：5

作者：

Bogopolski, O. ^{[1
,2
]}

机构：

[1] Univ Dusseldorf, D-40225 Dusseldorf, Germany

[2] Russian Acad Sci, Inst Math, Siberian Branch, Novosibirsk 630090, Russia

来源：

COMMUNICATIONS IN ALGEBRA | 2012年 / 40卷 / 07期

关键词：

Automorphisms; Baumslag-Solitar groups; Commensurators; Quasi-isometry;

D O I：

10.1080/00927872.2011.580440

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove that for any n >= 2, the abstract commensurator group of the Baumslag-Solitar group BS(1, n) is isomorphic to the subgroup {((0) (1)(p) (q)) vertical bar q is an element of Q, p is an element of Q*} of GL(2)(Q). We also prove that for any finitely generated group G with the unique root property the natural homomorphisms Aut(G) -> Comm(G) -> QI(G) are embeddings.

引用

页码：2494 / 2502

页数：9

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