Character Correspondences and Subgroups of Operator Groups

✍ Scribed by Christopher Puin

• Publisher: Elsevier Science
• Year: 1998
• Tongue: English
• Weight: 189 KB
• Volume: 207
• Category: Article
• ISSN: 0021-8693
• DOI: 10.1006/jabr.1998.7495

✦ Synopsis

Let A and G be finite groups with coprime orders, and suppose that A acts on G by automorphisms. Let π G A Irr A G → Irr C G A be the Glauberman-Isaacs correspondence. Let B ≤ A and let χ ∈ Irr A G . We examine the conjecture that χπ G A is an irreducible constituent of the restriction of χπ G B to C G A and show that it is valid if G is supersolvable. Then, we show when the analog of this conjecture for Brauer characters and the Uno-Wolf correspondence holds.