Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On finite groups whose derived subgroup has bounded rank   Let $G$ be a finite group with derived subgroup of rank $r$. We prove that
$\gzz\leq |G'|^{2r}$. Motivated by the results of I. M. Isaacs in \cite{isa} we
show that if $G$ is capable then $\gz\leq |G'|^{4r}$. This answers a question
of L. Pyber. We prove that if $G$ is a capable $p$-group then the rank of
$G/\mathbf{Z}(G)$ is bounded above in terms of the rank of $G'$.

18
The categories of this paper are: econ
24
The categories of this paper are: dg-ga
11
The categories of this paper are: hep-lat
29
The categories of this paper are: funct-an
9
The categories of this paper are: nlin
23
The categories of this paper are: solv-int
32
The categories of this paper are: atom-ph
3
The categories of this paper are: physics
22
The categories of this paper are: chao-dyn
33
The categories of this paper are: plasm-ph
8
The categories of this paper are: hep-ex
27
The categories of this paper are: comp-gas
31
The categories of this paper are: ao-sci
7
The categories of this paper are: hep-th
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The categories of this paper are: quant-ph
28
The categories of this paper are: alg-geom