Some criteria concerning the rational vanishing of Whitehead groups

Wolfgang Lueck; Bob Oliver

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arXiv · 2506.22906

Some criteria concerning the rational vanishing of Whitehead groups

Wolfgang Lueck·Bob Oliver

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Abstract

We give several examples of finite groups $G$ for which the rank of the tensor product $\mathbb{Z} \otimes_{\mathbb{Z}\mathrm{Aut}(G)}$ Wh$(G)$ is or is not zero. This is motivated by an earlier theorem of the first author, which implies as a special case that when this group has nonzero rank, the Whitehead group of any other group (finite or infinite) that contains $G$ as a normal subgroup is rationally nontrivial.

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Wolfgang Lueck, Bob Oliver. 2025-06-28. Some criteria concerning the rational vanishing of Whitehead groups. https://arxiv.org/abs/2506.22906

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