Summary: An abelian group \(G\) is called a \(TI\)-group if every associative ring with additive group \(G\) is filial. An abelian group \(G\) such that every (associative) ring with additive group \(G\) is an \(SI\)-ring (a hamiltonian ring) is called an \(SI\)-group (an \(SI_H\)-group). In this paper, \(TI\)-groups, as well as \(SI\)-groups and \(SI_H\)-groups are described in the class of reduced algebraically compact abelian groups.