A solvable counterexample to the Hambleton-Taylor-Williams Conjecture

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.