Work

A note on non-solvable groups with given number of particular subgroups

Year: 2024

Type: article

Abstract: Considering the quantitative properties of some particular subgroups of a finite group, we prove that (1) a non-solvable group $G$ has exactly 5 non-subnormal non-supersolvable proper subgroups if and only if $G\cong A_5$ or $SL_2(5)$. (2) a non-solvable group $G$ has exactly 5 non-subnormal non-2-nilpotent proper subgroups if and only if $G\cong A_5$ or $SL_2(5)$. (3) a non-solvable group $G$ has exactly 16 non-subnormal non-2-closed proper subgroups (or two same order classes of non-subnormal non-2-closed proper subgroups) if and only if $G\cong A_5$ or $SL_2(5)$. Our results improve some known related research.

Source: Proceedings of the Romanian Academy Series A Mathematics Physics Technical Sciences Information Science

DOI: 10.59277/pra-ser.a.25.4.04

Authors: Jiangtao SHI, Fanjie XU, Yifan LIU

Institution: Yantai University

Language: English

Topic: Finite Group Theory Research

Subfield: Discrete Mathematics and Combinatorics

Field: Mathematics

Domain: Physical Sciences

Open Access status: bronze

Funders: National Natural Science Foundation of China, Natural Science Foundation of Shandong Province

Awards: G4610495414, G6075970929