Sylow subgroups for distinct primes and intersection of nilpotent subgroups
Abstract
Let G be a finite group and let ( P i ) i = 1 n be Sylow subgroups for distinct primes p 1 , … , p n . We conjecture that there exists x ∈ G such that P i ∩ P i x is inclusion-minimal in { P i ∩ P i g : g ∈ G } for all i . As a first step in this direction, we show that a finite group cannot be covered by (proper) Sylow normalizers for distinct primes. Then we settle the conjecture in two opposite situations: symmetric and alternating groups of large degree and metanilpotent groups of odd order. Applications concerning the intersections of nilpotent subgroups are discussed.
Fields of Study & Subjects
Finite Group Theory Research
Rings
Modules
and Algebras
graph theory and CDMA systems
Publication details
- Journal / source
- Journal of Algebra
- Publisher
- Elsevier BV
- Volume
- 693
- Pages
- 824–837
- Publication date
- 28 January 2026
- Language
- EN