On infinitely supported groups

Abstract In the present article we define infinitely supported groups and investigate main properties of such groups, especially in abelian case. We give some examples in non-abelian case. We see that some celebrated constructions of groups are infinitely supported such as Čarin’s groups with min -n, Ol’shanskiǐ’s and Obraztsov’s constructions, Heineken-Mohamed type groups and non-perfect minimal non- FC -groups.