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arXiv · 1610.01510

A solvable counterexample to the Hambleton-Taylor-Williams Conjecture

Julia Semikina
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Abstract

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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Julia Semikina. 2016-10-05. A solvable counterexample to the Hambleton-Taylor-Williams Conjecture. https://arxiv.org/abs/1610.01510

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