Geodesic
AT-groups that are not AT-subgroups: Transition from $AT_{\omega}$-groups to $AT_{\Omega}$-groups
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 28 (2022) no. 1, pp. 218-231 Cet article a éte moissonné depuis la source Math-Net.Ru

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Periodic nonlocally finite (Burnside) groups of infinite period are studied. The first explicit example of such groups was proposed by S.V. Aleshin in 1972. His construction was generalized to AT-groups, i.e., tree automorphism groups. A number of known problems have been solved with the help of AT-groups. Up to now, in reality, only the class of $AT_{\omega}$-groups, i.e., the class of AT-groups over a sequence of cyclic groups of prime order, has been studied. In this paper, the class of $AT_{\Omega}$-groups, i.e., of AT-groups over a sequence of cyclic groups of arbitrary finite order, is studied. The difference between $AT_{\omega}$-groups and true $AT_{\Omega}$-groups was revealed by the solution of the Kourovka Problem 16.79. The study of the class of $AT_{\Omega}$-groups has allowed us to introduce a number of new notions. Now the $AT_{\omega}$-groups can be considered as elementary AT-groups by which the AT-groups over a sequence of periodic groups are saturated. We propose a strategy for studying such AT-groups and give promising directions of this kind of research.
Keywords: Burnside groups, residually finite group, finiteness conditions, AT-groups, trees, wreath product. 
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A. V. Rozhkov. AT-groups that are not AT-subgroups: Transition from $AT_{\omega}$-groups to $AT_{\Omega}$-groups. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 28 (2022) no. 1, pp. 218-231. http://geodesic.mathdoc.fr/item/TIMM_2022_28_1_a14/

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