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Published online by Cambridge University Press: 11 January 2016
We consider the problem of whether the norm one torus defined by a finite separable field extension K/k is stably (or retract) rational over k. This has already been solved for the case where K/k is a Galois extension. In this paper, we solve the problem for the case where K/k is a non-Galois extension such that the Galois group of the Galois closure of K/k is nilpotent or metacyclic.