Locally finite groups containing direct products of dihedral groups
Algebra i logika, Tome 63 (2024) no. 3, pp. 323-337
Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

Let $d$ be a fixed natural number. We prove the following: THEOREM. Let $G$ be a locally finite group saturated with groups from a set $\mathfrak{M}$ consisting of direct products of $d$ dihedral groups. Then $G$ is a direct product of $d$ groups of the form $B\leftthreetimes\langle v\rangle$, where $B$ is a locally cyclic group inverted by an involution $v$.
Keywords: locally finite group, direct products of dihedral groups, locally cyclic group, involution.
@article{AL_2024_63_3_a6,
     author = {A. A. Shlepkin},
     title = {Locally finite groups containing direct products of dihedral groups},
     journal = {Algebra i logika},
     pages = {323--337},
     year = {2024},
     volume = {63},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_2024_63_3_a6/}
}
TY  - JOUR
AU  - A. A. Shlepkin
TI  - Locally finite groups containing direct products of dihedral groups
JO  - Algebra i logika
PY  - 2024
SP  - 323
EP  - 337
VL  - 63
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/AL_2024_63_3_a6/
LA  - ru
ID  - AL_2024_63_3_a6
ER  - 
%0 Journal Article
%A A. A. Shlepkin
%T Locally finite groups containing direct products of dihedral groups
%J Algebra i logika
%D 2024
%P 323-337
%V 63
%N 3
%U http://geodesic.mathdoc.fr/item/AL_2024_63_3_a6/
%G ru
%F AL_2024_63_3_a6
A. A. Shlepkin. Locally finite groups containing direct products of dihedral groups. Algebra i logika, Tome 63 (2024) no. 3, pp. 323-337. http://geodesic.mathdoc.fr/item/AL_2024_63_3_a6/

[1] A. K. Shlepkin, “Sopryazhenno biprimitivno konechnye gruppy, soderzhaschie konechnye nerazreshimye podgruppy”, III mezhd. konf. po algebre pamyati M. I. Kargapolova, Sb. tez. (Krasnoyarsk, 23–28 avg. 1993), Krasnoyarsk, 1993, 369

[2] A. K. Shlepkin, “O nekotorykh periodicheskikh gruppakh, nasyschennykh konechnymi prostymi gruppami”, Matem. tr., 1:1 (1998), 129–138

[3] I. N. Belousov, A. S. Kondratev, A. V. Rozhkov, “XII shkola-konferentsiya, posvyaschennaya 65-letiyu so dnya rozhdeniya A.A. Makhneva (informatsionnaya statya)”, Tr. IMM UrO RAN, 24, no. 3, 2018, 281–285

[4] B. Amberg, L. Kazarin, “Periodic groups saturated by dihedral subgroups”, Abstr. int. algeb. conf. ded. to 70-th birthday of A. Yakovlev, Saint-Petersburg, 2010, 79–80

[5] D. V. Lytkina, V. D. Mazurov, “O periodicheskikh gruppakh s konechnoi netrivialnoi silovskoi 2-podgruppoi”, Tr. IMM UrO RAN, 29, no. 4, 2023, 146–154

[6] I. A. Timofeenko, A. A. Shlepkin, “O pryamykh proizvedeniyakh grupp diedra v lokalno konechnykh gruppakh”, Izv. Irkutskogo gos. un-ta. Ser. Matem., 47 (2024), 137–146

[7] A. V. Kukharev, A. A. Shlepkin, “Lokalno konechnye gruppy, nasyschennye pryamym proizvedeniem dvukh konechnykh grupp diedra”, Izv. Irkutskogo gos. un-ta. Ser. Matem., 44 (2023), 71–81