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

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{TIMM_2023_29_4_a19,
     author = {A. V. Rozhkov and V. Yu. Barsukova},
     title = {AT-groups},
     journal = {Trudy Instituta matematiki i mehaniki},
     pages = {241--258},
     publisher = {mathdoc},
     volume = {29},
     number = {4},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TIMM_2023_29_4_a19/}
}
TY  - JOUR
AU  - A. V. Rozhkov
AU  - V. Yu. Barsukova
TI  - AT-groups
JO  - Trudy Instituta matematiki i mehaniki
PY  - 2023
SP  - 241
EP  - 258
VL  - 29
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TIMM_2023_29_4_a19/
LA  - ru
ID  - TIMM_2023_29_4_a19
ER  - 
%0 Journal Article
%A A. V. Rozhkov
%A V. Yu. Barsukova
%T AT-groups
%J Trudy Instituta matematiki i mehaniki
%D 2023
%P 241-258
%V 29
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TIMM_2023_29_4_a19/
%G ru
%F TIMM_2023_29_4_a19
A. V. Rozhkov; V. Yu. Barsukova. AT-groups. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 29 (2023) no. 4, pp. 241-258. http://geodesic.mathdoc.fr/item/TIMM_2023_29_4_a19/