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.

Cite: Galt A.A. , Tyutyanov V.N.
G-permutable Subgroups in PSL2(q) and Hereditarily G-permutable Subgroups in PSU3(q)
Известия Иркутского государственного университета. Серия: Математика (Bulletin of Irkutsk State University. Series Mathematics). 2025. V.53. P.156-164. DOI: 10.26516/1997-7670.2025.53.156

Dates:

Submitted:	Jan 31, 2025
Accepted:	Mar 21, 2025
Published print:	Sep 18, 2025
Published online:	Sep 18, 2025

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