WEIGHT CONJECTURES FOR FUSION SYSTEMS ON AN EXTRASPECIAL GROUP
Abstract
Abstract In a previous paper, we stated and motivated counting conjectures for fusion systems that are purely local analogues of several local-to-global conjectures in the modular representation theory of finite groups. Here, we verify some of these conjectures for fusion systems on an extraspecial group of order $p^3$ , which contain among them the Ruiz–Viruel exotic fusion systems at the prime $7$ . As a byproduct, we verify Robinson’s ordinary weight conjecture for principal p -blocks of almost simple groups G realizing such (nonconstrained) fusion systems.
Fields of Study & Subjects
Finite Group Theory Research
Advanced Algebra and Geometry
Advanced Operator Algebra Research
Publication details
- Journal / source
- Journal of the Australian Mathematical Society
- Publisher
- Cambridge University Press (CUP)
- Volume
- 120
- Issue
- 3
- Pages
- 373–393
- Publication date
- 2 February 2026
- Language
- EN