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Let G be a commutative algebraic group over Q. Let Gamma be a subgroup ofG(Q) contained in the union of the compact subgroups of G(Q_p). We formulate aguess for the dimension of the closure of Gamma in G(Q_p), and show that itscorrectness for certain tori is equivalent to Leopoldt's conjecture.

The p-adic closure of a subgroup of rational points on a commutative algebraic group