代数和数理逻辑的问题。S. I. Adian的科学遗产

IF 1.4 4区数学 Q1 MATHEMATICS

Russian Mathematical Surveys Pub Date : 2021-01-01 DOI:10.1070/RM9980

V. S. Atabekyan, L. Beklemishev, V. Guba, I. Lysenok, A. Razborov, A. L. Semenov

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引用次数: 0

摘要

本文综述了Burnside问题和Burnside群的性质、群恒等式的有限基问题、群的周期积和Malcev问题、具有特殊性质群的构造(Tarski怪)、Burnside- Magnus问题中的构造界以及算法问题:群性质的识别问题、具有一种关系的半群的词问题和半图系统。重点是在Adian和他的学生的论文中获得的最重要的结果。参考书目:81种。

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Questions in algebra and mathematical logic. Scientific heritage of S. I. Adian

This is a survey of results on the Burnside problem and properties of Burnside groups, the finite basis problem for group identities, periodic products of groups and Malcev’s problem, construction of groups with special properties (Tarski monsters), constructive bounds in the Burnside- Magnus problem, and algorithmic problems: the problem of recognition of group properties, the word problem for semigroups with one relation, and semi-Thue systems. The focus is on the most important results obtained in papers of Adian and his students. Bibliography: 81 titles.

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来源期刊

Russian Mathematical Surveys 数学-数学

CiteScore

1.70

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Russian Mathematical Surveys is a high-prestige journal covering a wide area of mathematics. The Russian original is rigorously refereed in Russia and the translations are carefully scrutinised and edited by the London Mathematical Society. The survey articles on current trends in mathematics are generally written by leading experts in the field at the request of the Editorial Board.