Let $A$ and $B$ be subgroups of a finite group $G$. Then the subgroup $A$ is called: isoorderly permutable with $B$ if there is a subgroup $C$ of $G$ such that $|C| = |B|$ and $AC = CA$, hereditarily isoorderly permutable with $B$ if $A$ is isoorderly permutable with $B$ in any subgroup of $G$ containing $A$ and $B$, isoorderly permutable in $G$ if $A$ is isoorderly permutable with every subgroup of $G$, and hereditarily isoorderly permutable in $G$ if $A$ is hereditarily isoorderly permutable with every subgroup of $G$. In this paper, the properties of isoorderly permutable subgroups are analyzed, and the structure of a finite group $G$ all of whose minimal subgroups are hereditarily isoorderly permutable is studied.
Keywords: finite group, isoorderly permutable subgroup, hereditarily isoorderly permutable subgroup, minimal subgroup
Received August 23, 2024
Revised October 8, 2024
Accepted October 14, 2024
Published online: November 1, 2024
Funding Agency: The research of the second and of the third authors was supported by the Russian Science Foundation and by the Belarusian Republican Foundation for Fundamental Research (project no. Φ23PHΦ-237).
Xiaolan Yi, Zhejiang Sci-Tech University, Hangzhou, P. R. China, e-mail: yixiaolan2005@126.com
Sergei Fedorovich Kamornikov, Dr. Phys.-Math. Sci., Prof., F. Skorina Gomel State University, Gomel, 246028 Republic of Belarus, e-mail: sfkamornikov@mail.ru
Valentin Nikolayevich Tyutyanov, Dr. Phys.-Math. Sci., Prof., Gomel Branch of International University “MITSO”, Gomel, 246029 Republic of Belarus, e-mail: vtutanov@gmail.com
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Cite this article as: X. Yi, S.F. Kamornikov, V.N. Tyutyanov. Isoorderly permutable subgroups of finite groups. Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2025, vol. 31, no. 1, pp. 66–76.
