足够大秩的自由幂零群$l\geqslant 2$的子群隶属问题的不可判定性

IF 0.8 3区数学 Q2 MATHEMATICS

Izvestiya Mathematics Pub Date : 2023-01-01 DOI:10.4213/im9342e

Vitalii Anatol'evich Roman'kov

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引用次数: 0

摘要

给出了M. Lohrey和B. Steinberg关于有限生成的幂零群的子群隶属问题的可决性问题的答案。即构造了秩为$r$的自由幂零群$2$的有限生成子群，其隶属性问题在算法上是不可确定的。这意味着在秩为$r$的任意类$l \geqslant 2$的自由幂零群中存在一个具有类似性质的子拟群。这个证明是基于希尔伯特第十题的不可判定性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Undecidability of the submonoid membership problem for free nilpotent group of class $l\geqslant 2$ of sufficiently large rank

An answer is given to the question of M. Lohrey and B. Steinberg on decidability of the submonoid membership problem for a finitely generated nilpotent group. Namely, a finitely generated submonoid of a free nilpotent group of class $2$ of sufficiently large rank $r$ is constructed, for which the membership problem is algorithmically undecidable. This implies the existence of a submonoid with similar property in any free nilpotent group of class $l \geqslant 2$ of rank $r$. The proof is based on the undecidability of Hilbert's tenth problem.

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来源期刊

Izvestiya Mathematics 数学-数学

CiteScore

1.30

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： The Russian original is rigorously refereed in Russia and the translations are carefully scrutinised and edited by the London Mathematical Society. This publication covers all fields of mathematics, but special attention is given to: Algebra; Mathematical logic; Number theory; Mathematical analysis; Geometry; Topology; Differential equations.