On groups satisfying the double chain condition on nonascendant subgroups

Abstract

If $\theta$ is a subgroup property, a group $G$ is said to satisfy the double chain condition on $\theta$-subgroups if it admits no infinite double chain $$\cdots<X_{-n}<\cdots<X_{-1}<X_0<X_1<\cdots<X_n<\cdots$$ consisting of $\theta$-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.

Keywords

• double chains
• ascendant subgroups
• locally finite groups
• locally nilpotent groups