# "On the Taketa bound for normally monomial p-groups of maximal class"

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## Authors

Keller, Thomas Michael

Ragan, Dustin

Tims, Geoffrey T.

## Issue Date

2004-07-15

## Type

Article

## Language

en_US

## Keywords

Lie algebra , Taketa bound , P-groups , Finite monomial groups , Algebra

## Alternative Title

## Abstract

A longstanding problem in the representation theory of finite solvable groups, sometimes called the Taketa problem, is to find strong bounds for the derived length dl(G) in terms of the number |cd(G)| of irreducible character degrees of the group G. For p-groups an old result of Taketa implies that dl(G)|cd(G)|, and while it is conjectured that the true bound is much smaller (in fact, logarithmic) for large dl(G), it turns out to be extremely difficult to improve on Taketa's bound at all. Here, therefore, we suggest to first study the problem for a restricted class of p-groups, namely normally monomial p-groups of maximal class. We exhibit some structural features of these groups and show that if G is such a group, then .

## Description

Geoffrey T. Tims is a 2003 graduate of the Department of Mathematics and Computer Science, Drake University.

## Citation

JOURNAL OF ALGEBRA, July 2004. 277 (2): 675-688.

## Publisher

Elsevier Science

## License

## Journal

## Volume

## Issue

## PubMed ID

## DOI

## ISSN

0021-8693