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«THE BULLETIN OF IRKUTSK STATE UNIVERSITY». SERIES «MATHEMATICS»
«IZVESTIYA IRKUTSKOGO GOSUDARSTVENNOGO UNIVERSITETA». SERIYA «MATEMATIKA»
ISSN 1997-7670 (Print)
ISSN 2541-8785 (Online)

List of issues > Series «Mathematics». 2024. Vol 48

Layer-finiteness of Some Groups

Author(s)
Vladimir I. Senashov1

1Institute of Computational Modelling SB RAS, Krasnoyarsk, Russian Federation

Abstract
Infinite groups with finiteness conditions for an infinite system of subgroups are studied. Groups with a condition: the normalizer of any non-trivial finite subgroup is a layer-finite group or the normalizer of any non-trivial finite subgroup has a layer-finite periodic part are studied for beginning in the locally finite class of group, then in the class of periodic groups of Shunkov and finally in the class of Shunkov groups which are contain a strongly embedded subgroup with an almost layer-finite periodic part. The group 𝐺 is called the Shunkov group if for any prime 𝑝 and for every finite subgroups 𝐻 from 𝐺 any two conjugate elements of order 𝑝 from the factor-group 𝑁𝐺(𝐻)/𝐻 generate a finite subgroup. Results for almost layer-finite groups and groups with almost layer-finite periodic part are transferred to layer-finite groups and groups with layer-finite periodic part. New characterizations of layer-finite groups and groups with layer-finite periodic part are obtained.
About the Authors
Vladimir I. Senashov, Dr. Sci. (Phys.–Math.), Prof., Institute of Computational Modelling SB RAS, Krasnoyarsk, 660036, Russian Federation, sen1112home@mail.ru
For citation

Senashov V. I. Layer-finiteness of Some Groups. The Bulletin of Irkutsk State University. Series Mathematics, 2024, vol. 48, pp. 145–151. https://doi.org/10.26516/1997-7670.2024.48.145

Keywords
periodic part, layer-finite group, almost layer-finite group, Shunkov group
UDC
519.45
MSC
20F99
DOI
https://doi.org/10.26516/1997-7670.2024.48.145
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