The extension of the first main theorem for \(\pi\)-blocks.
type: Item
instance of: scholarly article
title: The extension of the first main theorem for \(\pi\)-blocks.
zbMATH Open document ID: 1117.20008
published in: Science in China. Series A
publication date: 2007-01-24T00:00:00Z
review text: Let \(\pi\) be a set of primes, and let \(D\) be a normal \(\pi\)-subgroup of a finite \(\pi\)-separable group \(G\). The author shows that the \(\pi\)-blocks of \(G\) with defect group \(D\) are in bijection with the \(G\)-orbits of \(\pi\)-blocks \(b\) of \(H=DC_G(D)\) with defect group \(D\) such that \(|I_G(b):H|_\pi=1\); here \(I_G(b)\) denotes the stabilizer of \(b\) in \(G\).
Mathematics Subject Classification ID: 20C20
zbMATH DE Number: 5118295
zbMATH Keywords: blocks
zbMATH Keywords: defect groups
zbMATH Keywords: finite \(\pi\)-separable groups
author: Jinke Hai
reviewed by: Burkhard Külshammer
MaRDI profile type: Publication
full work available at URL: s11425-006-0620-9
OpenAlex ID: W1553010039
cites work: Characters of \(\pi\)-separable groups
cites work: Character correspondences and irreducible induction and restriction
cites work: Q3826736
cites work: On π-blocks of finite groups
cites work: pi-blocks of pi-separable groups. I
cites work: pi-blocks of pi-separable groups. II
cites work: Character correspondences in solvable groups
cites work: \(\pi\)-blocks of characters in a finite group
DOI: 10.1007/S11425-006-0620-9
description: scientific article; zbMATH DE number 5118295