On Centres of 3-blocks of the Ree groups ²G₂(q)

2016/07/07 by Julian Brough, Brough, Julian, Inga Schwabrow +1 · 1 citation
Computer Science · Mathematics · #20C05 #20C20 #Algebraic Geometry and Number Theory #Coding theory and cryptography #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1607.02000

openalex publication_date 2016/07/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let G:=²G₂(q) be the simple Ree group with q=3^2k+1 and k a positive integer. We show that the centre of the principal block Z(kGe₀), where k is an algebraically closed field of characteristic 3, is not isomorphic to the centre of the Brauer corresponding block Z(kN_G(P)), where N_G(P) is the normaliser in G of a Sylow 3-subgroup. As part of the proof, we compute the conjugacy classes of elements and the character tables of the maximal parabolic subgroups of G.

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• Centres of blocks of finite groups with trivial intersection Sylow p-subgroups

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