AT-groups

A. V. Rozhkov   ; V. Yu. Barsukova

Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 29 (2023) no. 4, pp. 241-258

Résumé

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.

Détail

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

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