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Let $K/ \mathbb{Q}$ be an imaginary $S_3$-extension, and $p$ a prime numberwhich splits into exactly three primes in $K$. We give a sufficient conditionfor the validity of Greenberg's generalized conjecture for $K$ and $p$.

A remark on Greenberg's generalized conjecture for imaginary $S_3$-extensions of $\mathbb{Q}$