Work

On small Sylow numbers of finite groups

Year: 2025

Type: article

Abstract: Let G be a finite group. Let [Formula: see text] be the number of Sylow p-subgroups of G for some prime p. We prove that if [Formula: see text], then with few exceptions it is a prime power. We also prove that if [Formula: see text] and p is not a Mersenne prime greater than 3, then G is p-solvable if and only if [Formula: see text] is a prime power.

Source: International Journal of Algebra and Computation

DOI: 10.1142/s0218196725500146

Authors: Xiaofang Gao, Igor Lima, Rulin Shen

Institutions: Hubei University, Universidade de Brasília, Hubei University for Nationalities

Language: English

Topic: Finite Group Theory Research

Subfield: Discrete Mathematics and Combinatorics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: National Natural Science Foundation of China

Award: G226490736