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

## On the Existence of 𝑓-local Subgroups in a Group with Finite Involution

Author(s)
Anatoly I. Sozutov1, Mikhail V. Yanchenko1

1Siberian Federal University, Krasnoyarsk, Russian Federation

Abstract
An 𝑓-local subgroup of an infinite group is each its infinite subgroup with a nontrivial locally finite radical. An involution is said to be finite in a group if it generates a finite subgroup with each conjugate involution. An involution is called isolated if it does not commute with any conjugate involution. We study the group 𝐺 with a finite non-isolated involution 𝑖, which includes infinitely many elements of finite order. It is proved that 𝐺 has an 𝑓-local subgroup containing with 𝑖 infinitely many elements of finite order. The proof essentially uses the notion of a commuting graph.

Anatoly I. Sozutov, Dr. Sci. (Phys.–Math.), Prof., Institute of Mathematics and Computer Science, Siberian Federal University, Krasnoyarsk, 660041, Russian Federation, sozutov ai@mail.ru

Mikhail V. Yanchenko, Cand. Sci. (Phys.–Math.), Assoc. Prof., Institute of Mathematics and Computer Science, Siberian Federal University, Krasnoyarsk, 660041, Russian Federation, yanch1964@yandex.ru

For citation
Sozutov A. I., Yanchenko M. V.On the Existence of 𝑓-local Subgroups in a Group with Finite Involution. The Bulletin of Irkutsk State University. Series Mathematics, 2022, vol. 40, pp. 112–117.

https://doi.org/10.26516/1997-7670.2022.40.112

Keywords
group, 𝑓-local subgroup, finite involution, commuting graph
UDC
518.517
MSC
03C07, 03C60
DOI
https://doi.org/10.26516/1997-7670.2022.40.112
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