2-blocks with an abelian defect group and a freely acting cyclic inertial quotient

2020/10/16 by Cesare Giulio Ardito, Ardito, Cesare Giulio, Elliot Mckernon +1
Mathematics · Medicine · #FOS: Mathematics #Finite Group Theory Research #Geometric and Algebraic Topology #Group Theory (math.GR) #Parkinson's Disease and Spinal Disorders #Primary: 20C20. Secondary: 20C05 #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2010.08329

openalex publication_date 2020/10/16 · openalex created_date 2020/10/22 · openalex updated_date 2026/07/28

Abstract

We study blocks with an abelian defect group and a cyclic inertial quotient acting freely but not transitively. We prove that when p=2, such blocks are inertial, i.e. basic Morita equivalent to their Brauer correspondent. Together with a result of the second author on Singer cycle actions on homocyclic defect groups, this completes the classification of 2-blocks with a cyclic inertial quotient acting freely on an abelian defect group.

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