Simple groups with Brauer trees of principal blocks in the shape of a star

2021/05/08 by А. В. Кухарев, Kukharev, Andrei
Chemistry · Mathematics · Medicine · #Chronic Lymphocytic Leukemia Research #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #Representation Theory (math.RT) #Synthesis and Reactivity of Heterocycles

paper · pdf · doi:10.48550/arxiv.2105.03614

openalex publication_date 2021/05/08 · openalex created_date 2021/05/24 · openalex updated_date 2026/07/28

Abstract

We have found a list of finite simple groups with cyclic Sylow p-subgroup whose principal p-blocks have Brauer trees in the shape of a star, that is a tree of diameter at most 2. Moreover, for an arbitrary finite group G with cyclic Sylow p-subgroup, we have obtained a necessary condition when the Brauer tree of the principal p-block of G is a star.

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• The Brauer trees of unipotent blocks
• Blocks of profinite groups with cyclic defect group
• Brauer's problem 21 for principal blocks
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• p-Blocks Relative to a Character of a Normal Subgroup