"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