Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Finite Permutable Putcha Semigroups   A semigroup $S$ is called a permutable semigroup if $\alpha \circ \beta
=\beta \circ \alpha$ is satified for all congruences $\alpha$ and $\beta$ of
$S$. A semigroup is called a Putcha semigroup if it is a semilattice of
archimedean semigroups. In this paper we deal with finite permutable Putcha
semigroups. We describe the finite permutable archimedean semigroups and finite
permutable semigroups which are semilattices of a group and a nilpotent
semigroup.

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The categories of this paper are: nlin
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The categories of this paper are: solv-int
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The categories of this paper are: acc-phys
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The categories of this paper are: patt-sol
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The categories of this paper are: gr-qc
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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: quant-ph
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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: plasm-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: q-fin
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The categories of this paper are: hep-lat
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The categories of this paper are: dg-ga
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The categories of this paper are: q-bio