A note on codegrees and Taketa's inequality
| Autor: | Delfani, Mahtab, Ghasemi, Mohsen, Hekmatara, Somayeh |
|---|---|
| Rok vydání: | 2021 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | Let $G$ be a finite group and ${\rm cd}(G)$ will be the set of the degrees of the complex irreducible characters of $G$. Also let ${\rm cod}(G)$ be the set of codegrees of the irreducible characters of $G$. The Taketa problem conjectures if $G$ is solvable, then ${\rm dl}(G) \leq |{\rm cd}(G)|$, where ${\rm dl}(G)$ is the derived length of $G$. In this note, we show that ${\rm dl}(G) \leq |{\rm cod}(G)|$ in some cases and we conjecture that this inequality holds if $G$ is a finite solvable group. Comment: There is a mistake in the proof of lemma 3.1 |
| Databáze: | arXiv |
| Externí odkaz: |
|