Units of p-power order in principal p-blocks of p-constrained groups

2006/12/15 by Martin Hertweck, Hertweck, Martin
Mathematics · #16U60 (Primary) #20C05 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Finite Group Theory Research #Representation Theory (math.RT) #Rings and Algebras (math.RA) #math.RA #math.RT #msc:16U60 #msc:20C05

paper · pdf · doi:10.48550/arxiv.math/0612434

12 pages

arxiv created 2006/12/15 · openalex publication_date 2006/12/15 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let G be a finite group having a normal p-subgroup N that contains its centralizer C_G(N), and let R be a p-adic ring. It is shown that any finite p-group of units of augmentation one in RG which normalizes N is conjugate to a subgroup of G by a unit of RG, and if it centralizes N it is even contained in N.

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