Corpus ID: 235727467

A note on codegrees and Taketa's inequality

@inproceedings{Delfani2021ANO,
  title={A note on codegrees and Taketa's inequality},
  author={M. Delfani and Mohsen Ghasemi and Somayeh Hekmatara},
  year={2021}
}
Let G be a finite group and cd(G) will be the set of the degrees of the complex irreducible characters of G. Also let cod(G) be the set of codegrees of the irreducible characters of G. The Taketa problem conjectures if G is solvable, then dl(G) ≤ |cd(G)|, where dl(G) is the derived length of G. In this note, we show that dl(G) ≤ |cod(G)| in some cases and we conjecture that this inequality holds if G is a finite solvable group. 

References

SHOWING 1-10 OF 12 REFERENCES
Taketa's theorem for relative character degrees
It has been conjectured by Isaacs that, for finite group G, the inequality dl (N) ≤ |cd (G | N)| holds for all normal solvable subgroups N of G. We show that this conjecture holds for M -groups.Expand
Irreducible Character Degrees and Normal Subgroups
Let N be a normal subgroup of a finite group G and consider the set cd(G|N) of degrees of irreducible characters of G whose kernels do not contain N. A number of theorems are proved relating the setExpand
Character Theory of Finite Groups
1. (i) Suppose K is a conjugacy class of Sn contained in An; then K is called split if K is a union of two conjugacy classes of An. Show that the number of split conjugacy classes contained in An isExpand
Groups with few codegrees of irreducible characters
Abstract For a character χ of a finite group G, the number is called the codegree of χ. We also define . In this article, we give a characterization of finite groups with at most three codegrees ofExpand
Co-degrees of irreducible characters in finite groups☆
Abstract For a character χ of a finite group G, the number a ( χ ) : = | G : ker χ | / χ ( 1 ) is called the co-degree of χ. The object of this paper is to study the connection between the structureExpand
An Introduction to the Theory of Groups
Anyone who has studied "abstract algebra" and linear algebra as an undergraduate can understand this book. This edition has been completely revised and reorganized, without however losing any of theExpand
Some sufficient conditions for the Taketa inequality
In this study we have obtained some sufficient conditions for the Taketa inequality namely dlðG Þ�j cdðGÞj for finite solvable groups G.
{m
TLDR
The master programme in Applied Geology aims to provide comprehensive knowledge based on various branches of Geology, with special focus on Applied geology subjects in the areas of Geomorphology, Structural geology, Hydrogeology, Petroleum Geologists, Mining Geology), Remote Sensing and Environmental geology. Expand
S
  • Hekmatara Groups with few codegrees of irreducible characters, Comm. Algebra 47
  • 2019
Finite groups whose character graphs associated with codegrees have no triangle
  • Algebra Colloq 23(1)
  • 2016
...
1
2
...