Permutation modules over cyclic p-groups

2025/10/27 by Estanislau, Marlon · 1 citation
#20c11 #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2510.23759

Abstract

Let G be a cyclic p-group for some prime number p>0 and let R be a complete discrete valuation ring in mixed characteristic. In this paper, we present a generalization of two results that characterize RG-permutation modules, extending previous work by B. Torrecillas and Th. Weigel. Their original results were established under the assumption that p is unramified in R, whereas we extend their characterization to the case where p may be ramified. Unlike prior approaches, our proofs rely solely on fundamental facts from group cohomology and a version of Weiss' Theorem, avoiding deeper categorical techniques.

Citations

• On the geometry of lattices and finiteness of Picard groups
• On Picard groups of blocks with normal defect groups
• On Picard groups of blocks of finite groups
• Infinitely generated pseudocompact modules for finite groups and Weiss' Theorem
• Lattices and cohomological Mackey functors for finite cyclic p-groups

Cited by

• A recognition theorem for permutation modules over p-groups extending Weiss' Theorem

Related

• A recognition theorem for permutation modules over p-groups extending Weiss' Theorem
• Lattices and cohomological Mackey functors for finite cyclic p-groups
• Butler's Method applied to ℤ_p[C_p× C_p]-permutation modules
• Permutation presentations of modules over finite groups
• Infinitely generated pseudocompact modules for finite groups and Weiss' Theorem