Derived lengths of solvable groups having five irreducible character degrees. II. (Q698060)
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: Derived lengths of solvable groups having five irreducible character degrees. II. |
scientific article; zbMATH DE number 1802382
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Derived lengths of solvable groups having five irreducible character degrees. II. |
scientific article; zbMATH DE number 1802382 |
Statements
Derived lengths of solvable groups having five irreducible character degrees. II. (English)
0 references
18 September 2002
0 references
For definitions, see the preceding review Zbl 1040.20004 of part I. Let \(G\) be a solvable group with \(|\text{cd}(G)|=5\). Suppose that there is some prime \(p\) so that \(G/O^p(G)\) is not Abelian. Also, assume that \(\text{cd}(G)\) contains a degree \(>1\) which is not a multiple of \(p\). Under these hypotheses, \(\text{dl}(G)\leq 4\). This result is best possible as Theorem 5.1 shows.
0 references
solvable groups
0 references
derived lengths
0 references
character degrees
0 references
Taketa inequality
0 references
