Alperin's fusion theorem in terms of tame intersections
Explicit statement using the right-action convention
is a finite group, is a prime, and is a -Sylow subgroup of . Suppose are subsets of that are conjugate by some element . Then, there exists a collection of Tame Sylow intersection (?)s and a collection of elements such that:
- for any .
- Alperin's fusion theorem in terms of conjugation families: This is a somewhat weaker version.
- Alperin's fusion theorem in terms of well-placed tame intersections: This is a somewhat stronger version.