A note on the support of block idempotents
type: Item
instance of: scholarly article
title: A note on the support of block idempotents
zbMATH Open document ID: 0830.20018
DOI: 10.1007/BF01200433
author: Wolfgang Willems
published in: Archiv der Mathematik
publication date: 1995-04-18T00:00:00Z
review text: Let \(G\) be a finite group and \(K\) be a field of characteristic \(p\). For a block idempotent \(f\) of \(KG\) let \(O_f(G)\) denote the subgroup of \(G\) generated by the support of \(f\). It has been proved by \textit{G. Tiedt} [Beitr. Algebra Geom. 32, 47-51 (1991; Zbl 0784.20004)] that if \(G\) is a \(p\)-solvable group and \(f\) belongs to a block of maximal defect, then \(O_f (G) \leq O_{p'}(G)\). In earlier works, the author proved that for a principal block idempotent \(f\) the group \(O_f(G)\) is contained in the generalized \(p'\)-core \(O_{p^*} (G)\). In this paper the author generalizes his results and proves \(O_f (G) \leq O_{p^*} (G)\) whenever a defect group of \(f\) contains a Sylow \(p\)-subgroup of \(O_{p^*p} (G)\).
Mathematics Subject Classification ID: 20C20
Mathematics Subject Classification ID: 20C05
Mathematics Subject Classification ID: 20D20
Mathematics Subject Classification ID: 16S34
zbMATH DE Number: 743526
zbMATH Keywords: group algebra
zbMATH Keywords: finite group
zbMATH Keywords: \(p\)-solvable group
zbMATH Keywords: principal block idempotent
zbMATH Keywords: generalized \(p'\)-core
zbMATH Keywords: defect group
zbMATH Keywords: Sylow \(p\)-subgroup
reviewed by: M. R. Darafsheh
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 743526