Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A note on codegrees and Taketa's inequality   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.

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The categories of this paper are: q-bio
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The categories of this paper are: chao-dyn
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The categories of this paper are: atom-ph
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The categories of this paper are: econ
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The categories of this paper are: ao-sci
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The categories of this paper are: nucl-ex
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The categories of this paper are: physics
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The categories of this paper are: cs
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The categories of this paper are: q-alg
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The categories of this paper are: math-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: nucl-th
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The categories of this paper are: bayes-an
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The categories of this paper are: q-fin
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The categories of this paper are: cmp-lg
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The categories of this paper are: patt-sol