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In this paper, we prove the decidability of the theory of ℚp in the language (+, −,⋅, 0, 1, Pn(n ∈ ℕ)) expanded by a predicate for the multiplicative subgroup nℤ (where n is a fixed integer). There are two cases: if 
$v_p \left( n \right) > 0$ then the group determines a cross-section and we get an axiomatization of the theory and a result of quantifier elimination. If 
$v_p \left( n \right) = 0$, then we use the Mann property of the group to get an axiomatization of the theory.
