Character degrees and blocks of finite groups (Q2703580)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: Character degrees and blocks of finite groups |
scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Character degrees and blocks of finite groups |
scientific article |
Statements
Character degrees and blocks of finite groups (English)
0 references
7 March 2001
0 references
character degrees
0 references
\(p\)-blocks
0 references
\(\pi\)-separable groups
0 references
finite groups
0 references
irreducible characters
0 references
defect groups
0 references
Let \(G\) be a finite group, \(p\) and \(q\) be prime numbers and \(B\) be a \(p\)-block of \(G\). The authors prove that if \(G\) is \(\{p,q\}\)-separable and all irreducible characters of \(B\) have degrees not divisible by \(q\), then the defect group of \(B\) normalizes some Sylow \(q\)-subgroup of \(G\). This result is a \(p\)-block version of a theorem of Ito and Michler, and an example is given to show that the separability condition cannot be dropped.
0 references
