On the lifting of the Dade group

2018/07/12 by Lassueur, Caroline, Thévenaz, Jacques
#20C20 #FOS: Mathematics #Group Theory (math.GR) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1807.04487

Abstract

For the group of endo-permutation modules of a finite \(p\)-group, there is a surjective reduction modulo \(p\) homomorphism from a complete discrete valuation ring of characteristic 0 to its residue field of characteristic \(p\). We prove that this reduction map always has a section which is a group homomorphism.

Related

• Dade Groups for Finite Groups and Dimension Functions
• Discrete valuation rings, partitions and p-groups I
• Permutation modules over cyclic p-groups
• A recognition theorem for permutation modules over p-groups extending Weiss' Theorem
• Gluing endo-permutation modules