On Endo-trivial Modules for p-Solvable Groups

2010/07/20 by Gabriel Navarro, Navarro, Gabriel, Geoffrey R. Robinson +1
Mathematics · #20C20 #Advanced Topology and Set Theory #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #Representation Theory (math.RT) #Rings, Modules, and Algebras #math.GR #math.RT #msc:20C20

paper · pdf · doi:10.48550/arxiv.1007.3442

arxiv created 2010/07/20 · openalex publication_date 2010/07/20 · arxiv updated 2010/07/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove a conjecture of J. Carlson, N. Mazza and J. Thévenaz; namely, we will prove that if G is a finite p-nilpotent group which contains a non-cyclic elementary Abelian p-subgroup and k is an algebraically closed field of characteristic p, then all simple endo-trivial kG-modules are 1-dimensional.

Related

• On the orbit category on nontrivial p-subgroups and endotrivial modules
• Endo-trivial modules for finite groups with Klein-four Sylow 2-subgroups
• Completely simple endomorphism rings of modules
• Endo-trivial modules for finite groups with dihedral Sylow 2-subgroup
• The endomorphism ring of the trivial module in a localized category