A note on a recent paper of Iwasawa on the capitulation problem (Q913854)

It is shown that if \(p_ 1,...,p_{n-1}\) are prime numbers such that all Legendre symbols \((p_ i/p_ j)\) are equal 1, then one can find infinitely many primes \(p_ n\) with the property that the field \({\mathbb{Q}}((p_ 1... p_ n)^{1/2})\) has no units with negative norm. The author writes that this result is implicit in the work of \textit{L. Rédei} [J. Reine Angew. Math. 174, 15-55 (1935; Zbl 0013.00304)] but the proof given here is much simpler. He points out that the analytical part of the quoted paper contains serious errors.