Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Finite skew braces with solvable additive group   A. Smoktunowicz and L. Vendramin conjectured that if $A$ is a finite skew
brace with solvable additive group, then the multiplicative group of $A$ is
solvable. In this short note we make a step towards positive solution of this
conjecture proving that if $A$ is a minimal finite skew brace with solvable
additive group and non-solvable multiplicative group, then the multiplicative
group of $A$ is not simple. On the way to obtaining this result, we prove that
the conjecture of A. Smoktunowicz and L. Vendramin is correct in the case when
the order of $A$ is not divisible by $3$.

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The categories of this paper are: nucl-ex
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The categories of this paper are: astro-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: q-bio
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The categories of this paper are: bayes-an
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The categories of this paper are: supr-con
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The categories of this paper are: plasm-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: q-alg
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The categories of this paper are: econ
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The categories of this paper are: quant-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: eess
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The categories of this paper are: q-fin
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The categories of this paper are: cond-mat
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The categories of this paper are: stat