Quadratic equations in the Grigorchuk group

被引：13

作者：

Lysenok, Igor ^{[1
,2
]}

Miasnikov, Alexei ^{[2
]}

Ushakov, Alexander ^{[2
]}

机构：

[1] VA Steklov Math Inst, Gubkina Str 8, Moscow 119991, Russia

[2] Stevens Inst Technol, Dept Math, 1 Castle Point Terrace, Hoboken, NJ 07030 USA

来源：

GROUPS GEOMETRY AND DYNAMICS | 2016年 / 10卷 / 01期

基金：

俄罗斯基础研究基金会; 美国国家科学基金会;

关键词：

Grigorchuck group; Diophantine problem; quadratic equations;

D O I：

10.4171/GGD/348

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove that the Diophantine problem for quadratic equations in the Grigorchuk group is algorithmically solvable. As a corollary to our approach, we prove that the group has a finite commutator width.

引用

页码：201 / 239

页数：39

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