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Dedicated to Professor S. Naimpally on the occasion of his 70 th birthday.Abstract. Following [22] we study the class S of all groups that admit a small set of generators. Here we adopt also another notion of smallness (P -small) introduced by Prodanov in the case of abelian groups. We push further some results obtained in [22] (by adding some new members of S) and partially resolve an open question posed in [22]. We show that in most cases the groups in S admit a P -small set of generators.

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