Nilpotent $p\mspace{1mu}$-local finite groups

Abstract

In this paper we provide characterizations of p-nilpotency for fusion systems and p-local finite groups that are inspired by known result for finite groups. In particular, we generalize criteria by Atiyah, Brunetti, Frobenius, Quillen, Stammbach and Tate.1991 Mathematics Subject Classification. Primary 55R35, 20D15, Secondary 20D20, 20C20, 20N99.

On Thompson’s p-complement theorems for saturated fusion systems

“…These results contribute to the list of nilpotency criteria for saturated fusion systems that generalize classical criteria for finite groups, and fits within the framework of previous work by Kessar-Linckelmann [9], Díaz-Glesser-Mazza-Park [6], Díaz-Glesser-Park-Stancu [7], Cantarero-Scherer-Viruel [3] and Craven [5]. Indeed, Theorem 1.1 can also be deduced from [6,Corollary 4.6], although the proof of Thompson's pnilpotence criterion in [6] resorts to the group case, while the proof presented here is purely fusion theoretical.…”

A spectral sequence for fusion systems

“…This last result was already proven in [8] using transfer for fusion systems and in [5] by topological methods. Here the proof mimics Tate's cohomological original proof that relies on the five terms exact sequence associated to the LyndonHochschild-Serre spectral sequence but using instead the spectral sequence of Theorem 1.1.…”

A cohomological characterization of nilpotent fusion systems

“…Already several authors have provided fusion system counterparts to characterizations of p-nilpotency for finite groups, see [2], [3], [7], [9], [10], [11], [13] and [14]. In this work, we prove the fusion system version of a p-nilpotency criterion from the late 60's due to Wong [16] and Hoechsmann, Roquette and Zassenhaus [12].…”