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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». 2025. Vol 53

𝐺-permutable Subgroups in PSL2(𝑞) and Hereditarily 𝐺-permutable Subgroups in PSU3(𝑞)

Author(s)

Alexey A. Galt1, Valentin N. Tyutyanov2

1 Sobolev Institute of Mathematics SB RAS, Novosibirsk, Russian Federation 

2 MITSO International University, Gomel, Belarus

Abstract
The concept of 𝑋-permutable subgroup, introduced by A. N. Skiba, generalizes the classical concept of a permutable subgroup. Many classes of finite groups have been characterized in terms of 𝑋-permutable subgroups. In particular, W. Guo, A. N. Skiba and K. P. Shum obtained a characterization of the classes of solvable, supersolvable and nilpotent groups. Nevertheless, the further application of this concept in solving various problems in group theory is restrained by the lack of information about 𝐺-permutable and hereditarily 𝐺-permutable subgroups lying in the composition factors of groups. In this regard, the following problems were posed in the Kourovka Notebook: which finite nonabelian simple groups 𝐺 have a proper 𝐺-permutable subgroup and a proper hereditarily 𝐺-permutable subgroup? In this paper, an answer is obtained to the first question for simple linear groups of dimension two and to the second question for simple unitary groups of dimension three.
About the Authors

Alexey A. Galt, Cand. Sci. (Phys.Math.), Assoc. Prof., Sobolev Institute of Mathematics SB RAS, Novosibirsk, 630090, Russian Federation, galt84@gmail.com

Valentin N. Tyutyanov, Dr. Sci. (Phys.–Math.), Prof., MITSO International University, Gomel, 246029, Belarus, vtutanov@gmail.com

For citation

Galt A. A., Tyutyanov V. N. 𝐺-permutable Subgroups in PSL2(𝑞) and Hereditarily 𝐺-permutable Subgroups in PSU3(𝑞). The Bulletin of Irkutsk State University. Series Mathematics, 2025, vol. 53, pp. 156–164. https://doi.org/10.26516/1997-7670.2025.53.156

Keywords
simple linear group, simple unitary group, 𝐺-permutable subgroup, hereditarily 𝐺-permutable subgroup
UDC
512.542
MSC
20D06
DOI
https://doi.org/10.26516/1997-7670.2025.53.156
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