Published online by Cambridge University Press: 12 September 2018
If $\unicode[STIX]{x1D703}$ is a subgroup property, a group
$G$ is said to satisfy the double chain condition on
$\unicode[STIX]{x1D703}$-subgroups if it admits no infinite double sequences
$$\begin{eqnarray}\cdots <X_{-n}<\cdots <X_{-1}<X_{0}<X_{1}<\cdots <X_{n}<\cdots\end{eqnarray}$$
$\unicode[STIX]{x1D703}$-subgroups. We describe the structure of generalised radical groups satisfying the double chain condition on abelian subgroups.
The authors are members of GNSAGA-INdAM and this work was carried out within the ADV-AGTA project.