Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Central quotient versus commutator subgroup of groups   In 1904, Issai Schur proved the following result. If $G$ is an arbitrary
group such that $G/\Z(G)$ is finite, where $\Z(G)$ denotes the center of the
group $G$, then the commutator subgroup of $G$ is finite. A partial converse of
this result was proved by B. H. Neumann in 1951. He proved that if $G$ is a
finitely generated group with finite commutator subgroup, then $G/\Z(G)$ is
finite. In this short note, we exhibit few arguments of Neumann, which provide
further generalizations of converse of the above mentioned result of Schur. We
classify all finite groups $G$ such that $|G/\Z(G)| = |\gamma_2(G)|^d$, where
$d$ denotes the number of elements in a minimal generating set for $G/\Z(G)$.
Some problems and questions are posed in the sequel.

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The categories of this paper are: hep-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: q-alg
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The categories of this paper are: acc-phys
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The categories of this paper are: q-bio
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The categories of this paper are: cs
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The categories of this paper are: solv-int
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The categories of this paper are: patt-sol
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The categories of this paper are: dg-ga
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The categories of this paper are: supr-con
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The categories of this paper are: eess
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The categories of this paper are: gr-qc
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The categories of this paper are: plasm-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: alg-geom
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The categories of this paper are: hep-lat