Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A combinatorial problem arising in group theory   We consider a combinatorial problem occurring naturally in a group
theoretical setting and provide a constructive solution in a special case. More
precisely, in 1999 the author established a logarithmic bound for the derived
length of the quotient of a finite solvable group modulo the second Fitting
subgroup in terms of the number of irreducible character degrees of the group.
Along the way, in two key lemmas an inductive process was used which at its
core required a solution of some weak form of the combinatorial problem studied
in this paper. This problem can be stated and studied without any group
theoretical background, and in this paper we present the problem, discuss what
is known and what the main conjecture is, and solve the conjecture in the
smallest open case.

31
The categories of this paper are: ao-sci
36
The categories of this paper are: cmp-lg
35
The categories of this paper are: mtrl-th
21
The categories of this paper are: adap-org
18
The categories of this paper are: econ
5
The categories of this paper are: gr-qc
1
The categories of this paper are: cs
13
The categories of this paper are: quant-ph
32
The categories of this paper are: atom-ph
15
The categories of this paper are: nucl-ex
4
The categories of this paper are: cond-mat
0
The categories of this paper are: hep-ph
34
The categories of this paper are: chem-ph
33
The categories of this paper are: plasm-ph
24
The categories of this paper are: dg-ga
37
The categories of this paper are: supr-con