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The aim of this paper is to study the group of elliptic units of a cyclic extension $L$ of an imaginary quadratic field $K$ such that the degree $[L:K]$ is a power of an odd prime $p$ . We construct an explicit root of the usual top generator of this group, and we use it to obtain an annihilation result of the $p$ -Sylow subgroup of the ideal class group of $L$ .

Annihilators of the Ideal Class Group of a Cyclic Extension of an Imaginary Quadratic Field