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

V. S. Atabekyan^a, L. D. Beklemishev^bc, V. S. Guba^d, I. G. Lysenok^b, A. A. Razborov^eb, A. L. Semenov<sup>fg

a</sup> Yerevan State University
^b Steklov Mathematical Institute of Russian Academy of Sciences, Moscow
^c National Research University Higher School of Economics
^d Vologda State University
^e University of Chicago, Chicago, USA
^f Moscow State University
^g Moscow Institute of Physics and Technology (National Research University)

Abstract: 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.

Keywords: combinatorial theory of groups and semigroups, periodic groups, Burnside problem, finite basis problem, algorithmic problems, Adian–Rabin theorem.

UDC: 510+512.5

MSC: Primary 20--02, 03--02; Secondary 01--02, 01A70, 20--03

Received: 10.01.2021

DOI: 10.4213/rm9980

 English version: Russian Mathematical Surveys, 2021, 76:1, 1–27

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