On the theories of free solvable groups

被引：7
|
作者：
Chapuis, O [1 ]
机构：
[1] Univ Lyon 1, CNRS, Inst Girard Desargues, Batiment Math,43 Blvd 11 Novembre 1918, F-69622 Villeurbanne, France
来源：
JOURNAL OF PURE AND APPLIED ALGEBRA | 1998年 / 131卷 / 01期
关键词：
D O I：
10.1016/S0022-4049(98)00024-3
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We prove that the terms of the derived series of a free solvable group are definable by existential formulae. We use this result to prove some 'model theoretic' results about free solvable groups. For example, we prove that if Hilbert's 10th problem has a negative answer for the field of the rationals, then the universal theory of a noncyclic free solvable group of class greater than or equal to 3 is undecidable. (C) 1998 Elsevier Science B.V. All rights reserved.
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页码：13 / 24
页数：12
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