A.V. Rozhkov, V.Yu. Barsukova. AT-groups ... P. 241-258

Periodic nonlocally finite (Burnside) groups of infinite period are studied. The first explicitly given example of such a group was proposed by S. V. Aleshin in 1972. His construction was generalized to AT-groups, which are automorphism groups of trees. A number of well-known problems have been solved with the help of AT-groups. This work is a continuation and development of the previous article by one of the authors. A new strategy for studying AT-groups has been implemented. The examples of Alyoshin, Sushanskii, and Gupta, which have already become classical, but, as it turned out, are poorly studied, are reviewed again. A well-studied example of Grigorchuk’s 2-group is generalized and reviewed in a new way. New classes of AT-groups are introduced. Tasks for the hour of problems are proposed.

Keywords: Burnside groups, residually finite groups, finiteness conditions, AT-groups, trees, wreath products

Received September 24, 2023

Revised November 12, 2023

Accepted November 20, 2023

Alexander Vicktorovich Rozhkov, Dr. Phys.-Math. Sci., Prof., Kuban State University, Krasnodar, 350040 Russia, e-mail: ros@math.kubsu.ru

Victoria Yurievna Barsukova, Cand. Sci. (Phys.-Math.), Kuban State University, Krasnodar, 350040 Russia, e-mail: barsukova.v.y@gmail.com

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Cite this article as: A.V. Rozhkov, V.Yu. Barsukova. AT-groups. Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2023, vol. 29, no. 4, pp. 241–258.