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The main aim of this article is to compute all the moments of the number of pℓ-torsion elements in some type of finite abelian groups. The averages involved in these moments are those defined for the Cohen–Lenstra heuristics for class groups and their adaptation for Tate–Shafarevich groups. In particular, we prove that the heuristic model for Tate–Shafarevich groups is compatible with the recent conjecture...
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