Simple Modules for Groups with Abelian Sylow 2-Subgroups are Algebraic

2008/01/17 by David Craven, David A. Craven, Craven, David A.
Mathematics · #20C20 #Algebraic structures and combinatorial models #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.0801.2665

9 pages

openalex publication_date 2008/01/17 · arxiv created 2008/05/18 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let G be a finite group and let p be a prime. A module for G over a field of characteristic p is called algebraic if it satisfies a polynomial, with addition and multiplication given by direct sum and tensor product. In some sense, having this property is equivalent to the tensor structure being 'nice' for that module. In this paper we prove that if G is a group with abelian Sylow 2-subgroups, and p=2, then all simple modules for G are algebraic. We include the conjecture that this result holds for all abelian 2-blocks.

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