On groups satisfying the double chain condition on nonascendant subgroups - Jia Zhang (International Journal of Group Theory)
If $θ$ is a subgroup property, a group $G$ is said to satisfy the double chain condition on $θ$-subgroups if it admits no infinite double chain $$…<X_{-n}<…<X_{-1}<X_0<X_1<…<X_n<…$$ consisting of $θ$-subgroups. Here we want to describe the structure of locally finite and locally nilpotent groups satisfying the double chain condition on non-ascendant subgroups in term of chain conditions and of ascendant subgroups.