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.
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页码：1823 / 1841
页数：19
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