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.
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页码：2494 / 2502
页数：9
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