The characteristically invariant extending property for abelian groups (Q6637182)

The notion of FI-extending property of an abelian groups was introduced by \textit{G. E. Birkenmeier} et al. [Commun. Algebra 29, No. 2, 673--685 (2001; Zbl 0992.20039)]. An abelian group has the FI-extending property if every fully invariant subgroup is essential in a direct summand. The authors introduce the notion of CI-extending property. An abelian group \(G\) is said to have CI-extending property if every characteristic subgroup of G is essential in a direct summand. The authors find conditions under which a separable \(2\)-group has CI-extending property. For an arbitrary vector group \(G\) the conditions when the notion FI-property coinsaid with the ntion CI-property is obtained.