Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A solvable counterexample to the Hambleton-Taylor-Williams Conjecture   I. Hambleton, L. Taylor and B. Williams conjectured a general formula in
spirit of H. Lenstra for the decomposition of $G_n(RG)$ for any finite group
$G$ and noetherian ring $R.$ The conjectured decomposition was shown to hold
for some large classes of finite groups. D. Webb and D. Yao discovered that the
conjecture failed for the symmetric group $S_5$, but remarked that it still
might be reasonable to expect the HTW-decomposition for solvable groups. In
this paper we show that the solvable group $\mathrm{SL}(2,\mathbb{F}_3)$ is
also a counterexample to the conjectured HTW-decomposition. Furthermore, we
prove that for any finite group $G$ the rank of $G_1(\mathbb{Z}G)$ does not
exceed the rank of the expression in the HTW-decomposition.

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The categories of this paper are: quant-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: stat
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The categories of this paper are: funct-an
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The categories of this paper are: econ
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The categories of this paper are: hep-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: nucl-th
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The categories of this paper are: nlin
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The categories of this paper are: cond-mat
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The categories of this paper are: hep-ex
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The categories of this paper are: gr-qc
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The categories of this paper are: q-alg
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The categories of this paper are: nucl-ex
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The categories of this paper are: cmp-lg
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The categories of this paper are: cs