UDK 512.54
RELATIONSHIPS OF THE ALMOST LAYER FINITE GROUPS WITH SIMILAR GROUP CLASSES
V. I. Senashov
Siberian State Airspace University named after academician M. F. Reshetnev 31, Krasnoyarsky Rabochy Av., Krasnoyarsk, 660014, Russian Federation Institute of Computational Modelling of Siberian Branch of RAS 50/44, Akademgorodok, Krasnoyarsk, 660036, Russian Federation Siberian Federal University 79, Svobodniy Av., Krasnoyarsk, 660036, Russian Federation E-mail: sen1112home@mail.ru
This paper is devoted to the study of the relationships between classes of groups with finiteness conditions. Finite-ness conditions superimpose limitations on a number of elements of a certain order in a group, on the order of its elements and on the cardinality of conjugate classes. The paper provides examples of groups that share class of almost layer-finite groups and those close to that class of groups: layer-finite groups, periodic groups, Chernikov’s groups, locally normal groups and the groups with the finite classes of conjugate elements. We establish the properties of the relationships of the considered classes of groups. In particular, we prove the coincidence of the classes of almost layer-finite groups and Chernikov’s groups in the class of primary groups. Our results will be used in the study of infinite groups with finiteness conditions.
group, layer-finite radical, involution, layer-finiteness.
References
- Chernikov S. N. Dokl. Akad. Nauk SSSR. 1945, vol. 50, p. 71–74.
- Chernikov S. N. Gruppy s zadannymi svoystvami sistemy podgrupp (Group with the Given Properties of Subgroups Systems). Moscow, Nauka, 1980, 384 p.
- Senashov V. I. Sloyno konechnyye gruppy (Layer Finite Groups). Novosibirsk, Nauka, 1993, 158 p.
- Matematicheskaya entsiklopediya. Vol. 1. Moscow, Sovetskaya entsiklopediya Pabl., 1977, 1152 p.
- Chernikov S. N. Math. Sbornik. 1948, vol. 22 (64), p. 101–133.
- Senashov V. I. Trudy IMM UrO RAN. 2010, vol. 16, № 3, p 234–239.
- Senashov V. I. Ukrain. math. zhurn. 2012, vol. 64, № 3, p. 384–391.
- Senashov V. I. Vestnik SibGAU. 2013, № 1 (47), р. 74–79.
- Shunkov V. P. O vlozhenii primarnykh elementov v gruppe (On an Embedding of Primary Elements in a Group). Novosibirsk, Nauka Pabl., 1992, 132 p.
Senashov Sergey Ivanovich – Doctor of Phisical and Mathematical Sciences, professor, head of the Department of Information economic systems, Siberian State Aerospace University named after academician M. F. Reshetnev. E-mail: sen@sibsau.ru
