A normal subgroup of a strongly reductive subgroup is strongly reductive

✍ Scribed by Benjamin M.S. Martin

• Publisher: Elsevier Science
• Year: 2003
• Tongue: English
• Weight: 78 KB
• Volume: 265
• Category: Article
• ISSN: 0021-8693
• DOI: 10.1016/s0021-8693(03)00293-x

✦ Synopsis

Let H be a strongly reductive subgroup of a reductive linear algebraic group G over an algebraically closed field k. We prove that any closed normal subgroup N of H is also a strongly reductive subgroup of G. If G = GL n (k) then this is a consequence of Clifford's Theorem from representation theory.