"On the Taketa bound for normally monomial p-groups of maximal class"
Keller, Thomas Michael
Tims, Geoffrey T.
MetadataShow full item record
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 .
Geoffrey T. Tims is a 2003 graduate of the Department of Mathematics and Computer Science, Drake University.
Showing items related by title, author, creator and subject.
An Analysis of the Leader Behaviors of Career-Bound and Place-Bound Public School Superintendents in Iowa Wolf, Leland R. (Drake University, 1974-11)Two types of superintendents are defined in the literature. Place-bound superintendents are promoted from within their present systems; career-bound superintendents are elected from outside. This study was made to determine ...
A Proposed Curriculum in The Social Studies for Culturally-Deprived Students Attending the Upward Bound Program at Central College, Pella, Iowa during The Summer of 1967 Van Tuyl, John W. (Drake University, 1967-08)