Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Equations solvable by radicals in a uniquely divisible group   We study equations in groups G with unique m-th roots for each positive
integer m. A word equation in two letters is an expression of the form w(X,A) =
B, where w is a finite word in the alphabet {X,A}. We think of A,B in G as
fixed coefficients, and X in G as the unknown. Certain word equations, such as
XAXAX=B, have solutions in terms of radicals, while others such as XXAX = B do
not. We obtain the first known infinite families of word equations not solvable
by radicals, and conjecture a complete classification. To a word w we associate
a polynomial P_w in Z[x,y] in two commuting variables, which factors whenever w
is a composition of smaller words. We prove that if P_w(x^2,y^2) has an
absolutely irreducible factor in Z[x,y], then the equation w(X,A)=B is not
solvable in terms of radicals.

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The categories of this paper are: nucl-th
33
The categories of this paper are: plasm-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: dg-ga
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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: cmp-lg
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The categories of this paper are: stat
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The categories of this paper are: chao-dyn
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The categories of this paper are: acc-phys
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-th
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The categories of this paper are: adap-org
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The categories of this paper are: bayes-an
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The categories of this paper are: q-bio
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The categories of this paper are: ao-sci