Patrick Serwene

activity

20192025

collaborators

6 papers

math.RT2025

A reduction theorem for non-vanishing of Hochschild cohomology of block algebras and Happel's property

Patrick Serwene, Constantin-Cosmin Todea

In this short research note we obtain a reduction theorem for the non-vanishing of the first Hochschild cohomology of block algebras of finite groups with non-trivial defect groups…

math.RT2024

Weight conjectures for Parker--Semeraro fusion systems

Radha Kessar, Jason Semeraro, Patrick Serwene +1

We prove that the Parker--Semeraro systems satisfy six of the nine Kessar--Linckelmann--Lynd--Semeraro weight conjectures for saturated fusion systems. As a by-product we obtain th…

math.GR2024

Exotic Fusion System on a Subgroup of the Monster

Patrick Serwene

We prove that an exotic fusion system described by Grazian on a subgroup of the Monster group is block-exotic, thus proving that exotic and block-exotic fusion systems are the same…

math.GR2023

Proving a conjecture for fusion systems on a class of groups

Patrick Serwene

We prove the conjecture that exotic and block-exotic fusion systems coincide holds for all fusion systems on exceptional $p$ -groups of maximal nilpotency class, where $p \geq 5$ . T…

math.RT2022

Reduction Theorems for Generalised Block Fusion Systems

Patrick Serwene

We generalise the Third Main Theorem by Brauer, the First and Second Fong Reduction to generalised block fusion systems and apply the Second Fong Reduction to extend a result by Ca…

math.RT2019

Block-Exoticity of a Family of Exotic Fusion Systems

Patrick Serwene

We prove that each exotic fusion system $F$ on a Sylow $p$ -subgroup of $G_{2} (p)$ for an odd prime $p$ with $O_{p} (F) = 1$ is block-exotic. This gives evidence…