The principal block idempotent
type: Item
instance of: scholarly article
title: The principal block idempotent
zbMATH Open document ID: 0691.20006
DOI: 10.1007/BF01198215
author: Burkhard Külshammer
published in: Archiv der Mathematik
publication date: 1991-01-01T00:00:00Z
review text: Let F be a field of prime characteristic p, let G be a finite group, let \(B_ 0(FG)\) denote the principal block of FG, and let \(e_ 0(FG)\) denote the corresponding block idempotent. We write \(e_ 0(FG)=\sum_{g\in G}\epsilon_ gg\) with \(\epsilon_ g\in F\) for \(g\in G\). It is known that \(\epsilon_ g=0\) if g is p-singular. We show that \(| G_{p'}| \epsilon_ g=| \{(u,s)\in G_ p\times G_{p'}:\) \(us=g\}| l_ F\) if g is p-regular; here \(G_ p\) and \(G_{p'}\) denote the sets of p-elements and \(p'\)-elements in G. Brauer's Third Main Theorem is an immediate consequence of this result.
reviewed by: Burkhard Külshammer
Mathematics Subject Classification ID: 20C05
Mathematics Subject Classification ID: 20C20
Mathematics Subject Classification ID: 16S34
zbMATH DE Number: 4130640
zbMATH Keywords: finite group
zbMATH Keywords: principal block
zbMATH Keywords: block idempotent
zbMATH Keywords: p-regular
zbMATH Keywords: p-elements
zbMATH Keywords: Brauer's Third Main Theorem
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01198215
OpenAlex ID: W2023107773
description: scientific article; zbMATH DE number 4130640