Fitting heights of odd-order groups with few character degrees

✍ Scribed by Jeffrey M. Riedl

• Book ID: 104140821
• Publisher: Elsevier Science
• Year: 2003
• Tongue: English
• Weight: 235 KB
• Volume: 267
• Category: Article
• ISSN: 0021-8693
• DOI: 10.1016/s0021-8693(03)00386-7

✦ Synopsis

If G is any finite solvable group having a normal Sylow 2-subgroup (in particular, if |G| is odd) and satisfying |cd(G)| 5, where cd(G) is the set of ordinary irreducible character degrees of G, we show that the Fitting height of G does not exceed |cd(G)| -2. In case |cd(G)| = 5, this upper bound on the Fitting height of G is best-possible.