Groups with a small set of generators

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.

Keywords

• Group
• Large set
• Small set
• Permutation group
• Linear group
• Compact group
• Profinite group