2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/112604Let $p$ be a prime number and let $K$ be a finite extension of the field $\mathbb{Q}_p$ of $p$-adic numbers. Let $N$ be a fully ramified, elementary abelian extension of $K$. Under a mild hypothesis on the extension $N/K$, we show that every element of $N$ with valuation congruent mod $[N:K]$ to the largest lower ramification number of $N/K$ generates a normal basis for $N$ over $K$.In addition to some small notational changes, the title "On the valuation of normal basis generators" was changed. The paper is accepted by the Bulletin of the LMSNumber Theory11S15; 13B05text