Gauss Decomposition with Prescribed Semisimple Part: Short Proof

✍ Scribed by Vladimir Chernousov; Erich W. Ellers; Nikolai Gordeev

• Book ID: 102577351
• Publisher: Elsevier Science
• Year: 2000
• Tongue: English
• Weight: 144 KB
• Volume: 229
• Category: Article
• ISSN: 0021-8693
• DOI: 10.1006/jabr.2000.8310

✦ Synopsis

We give a uniform short proof of the fact that the intersection of every non-central conjugacy class in a Chevalley group and a big Gauss cell is non-empty and that this intersection contains elements with any prescribed semisimple part. The interest in this property stems at least in part from its relation to Ore's and Thompson's conjectures in the theory of finite groups.