COMPUTATION OF THE CENTRALIZER DIMENSION OF GENERALIZED BAUMSLAG-SOLITAR GROUPS

被引：4

作者：

Dudkin, Fedor Anatol'evich ^{[1
,2
]}

机构：

[1] Sobolev Inst Math, Pr Koptyuga 4, Novosibirsk 630090, Russia

[2] Novosibirsk State Univ, Pirogova St 2, Novosibirsk 630090, Russia

来源：

SIBERIAN ELECTRONIC MATHEMATICAL REPORTS-SIBIRSKIE ELEKTRONNYE MATEMATICHESKIE IZVESTIYA | 2018年 / 15卷

基金：

俄罗斯科学基金会;

关键词：

centralizer of set of elements; centralizer dimension; generalized Baumslag-Solitar group; Baumslag-Solitar group;

D O I：

10.33048/semi.2018.15.147

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

A finitely generated group G acting on a tree so that all vertex and edge stabilizers are infinite cyclic groups is called a generalized Baumslag-Solitar group (GBS group). The centralizer dimension of a group G is the maximal length of a descending chain of centralizers. In this paper we complete a description of centralizers for unimodular GBS groups. This allows us to find the centralizer dimension of all GBS groups and to establish a way to compute it.

引用

页码：1823 / 1841

页数：19

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