On extensions for Ree groups of type F₄

2013/04/09 by David I. Stewart, Stewart, David I.
Computer Science · Mathematics · #Coding theory and cryptography #FOS: Mathematics #Finite Group Theory Research #Geometric and Algebraic Topology #Group Theory (math.GR) #Representation Theory (math.RT) #math.GR #math.RT

paper · pdf · doi:10.48550/arxiv.1304.2544

6 pages; fills a hole in another paper

arxiv created 2013/04/09 · openalex publication_date 2013/04/09 · arxiv updated 2013/04/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let k be an algebraically closed field of characteristic p=2. Let G=F₄ be simply connected over k and let σ:G→ G be an endomorphism such that the fixed point set G(σ) is a Ree group. We show, using the methods of Bendel--Nakano--Pillen, that self-extensions of simple kG(σ)-modules vanish generically and that for all but the first few Ree groups of type F₄, the 1-cohomology for G(σ) with coefficients in simple kG-modules can be identified with the 1-cohomology for G with coefficients in (possibly different) simple G-modules.

Citations

• Bounding extensions for finite groups and Frobenius kernels

Cited by

• New graded methods in the homological algebra of semisimple algebraic groups

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