On groups that can be covered by conjugates of finitely many cyclic or procyclic subgroups

Abstract

Given a discrete (resp. profinite) group G, we define NCC(G)$$\textrm{NCC}(G)$$ to be the smallest number of cyclic (resp. procyclic) subgroups of G whose conjugates cover G. In this paper we determine all residually finite discrete groups with finite NCC and give an almost complete characterization of profinite groups with finite NCC.