  Motivated by their study of pro-p limit groups, D.H. Kochloukova and P.A.
Zalesskii formulated a question concerning the minimum number of generators
d(N) of a normal subgroup N of prime index p in a non-abelian limit group G
(cf. Question*). It is shown that the analogous question for the rational rank
has an affirmative answer (cf. Thm. A). From this result one may conclude that
the original question of D.H. Kochloukova and P.A. Zalesskii has an affirmative
answer if the abelianization G^{\ab} of G is torsion free and d(G)=d(G^{\ab})
(cf. Cor.~B), or if G has the IF-property (cf. Thm. C).
