On small Sylow numbers of finite groups
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.
Authors
- Igor Lima (ORCID: https://orcid.org/0000-0002-0346-2716)
- Rulin Shen (ORCID: https://orcid.org/0000-0002-2999-3259)
- Xiaofang Gao (ORCID: https://orcid.org/0000-0001-8106-7941)
Institutions
- Minzu University of China (CN)
- Universidade de Brasília (BR)
- Minda Hospital (CN)
- Hubei University (CN)
Publication Details
- Journal
- International Journal of Algebra and Computation
- Published
- 2025-04-11
- DOI
- https://doi.org/10.1142/s0218196725500146
- Citations
- 1
- Primary Topic
- Finite Group Theory Research
- Type
- article
- Field-Weighted Citation Impact
- 5.33