Geodesic
On some properties of adjoint groups of associative nil algebras
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 10 (2017) no. 4, pp. 503-508.

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Local stepped configuration of adjoint groups of associated nil algebras is proved. Problems 8.67, 9.76, 13.53 from Kourovka Notebook are partially solved. A number of new issues are formulated.
Keywords: associative algebra, locally step group.
Mots-clés : adjoint group 
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Anatoliy I. Sozutov; Inna O. Aleksandrova. On some properties of adjoint groups of associative nil algebras. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 10 (2017) no. 4, pp. 503-508. http://geodesic.mathdoc.fr/item/JSFU_2017_10_4_a10/

[1] A. I. Maltsev, “Generalized nilpotent algebras and their associated groups”, Mat. sbornik, 25 (1949), 347–366 (in Russian) | MR | Zbl

[2] E. S. Golod, “On nil-algebras and finitely approximable p-groups”, Izv. Akad. Nauk SSSR Ser. Mat., 28:2 (1964), 273–276 (in Russian) | MR

[3] A. Z. Ananyin, “Nil-algebra with non-radical tensor square”, Sib. mat. journal, 26:2 (1985), 192–194 (in Russian) | MR

[4] V. I. Senashov, V. P. Shunkov, Groups with limbs, Pub. house of SB RAS, Novosibirsk, 2001 | MR

[5] A. Smoktunowicz, “Simple nil ring exits”, Comm. Algebra, 30 (2002), 27–59 | DOI | MR | Zbl

[6] S. N. Chernikov, “About the product groups of finite rank”, Algebra i logica, 20:3 (1981), 315–329 (in Russian) | MR

[7] Kourovka notebook: Unsolved problems in group theory, American Mathematical Society, 1983

[8] V. P. Shunkov, “On one class of $p$-groups”, Algebra and logic, 9:4 (1970), 484–496 (in Russian) | DOI | MR

[9] A. Y. Olshansky, “An infinite group with subgroups of prime order”, Izv. Akad. Nauk SSSR Ser. Mat., 44:2 (1980), 309–321 (in Russian) | MR

[10] V. A. Sereda, A. I. Sozutov, “On associative nil-algebras and groups of Golod”, Proceedings of the XXI Inter-University Scientific and Technical Conference (April 2003), KrasGASA, Krasnoyarsk, 2003, 21–44 (in Russian)

[11] Y. P. Sysak, Abstracts of the 17th All-Russian Algebraic Conference (Minsk, 1983), v. 1, in Russian | MR

[12] A. I. Sozutov, N. M. Suchkov, N. G. Suchkova, Infinite groups with involutions, Siberian Federal University, Krasnoyarsk, 2011 (in Russian)

[13] M. Hall, Group theory, MacMillan, Co., New York, 1959 | MR

[14] M. I. Kargapolov, Y. I. Merzlyakov, Basics of group theory, Nauka, M., 1982 (in Russian) | MR

[15] N. S. Chernikov, Groups that are decomposable into a product of commuting subgroups, Naukova Dumka, Kiev, 1987 (in Russian) | MR

[16] V. M. Liauchuk, “Some locally nilpotent rings and their adjoined groups”, Mat. Zametki, 42:5 (1987), 631–641 (in Russian) | MR