\(\ell\)-groups with restricted conditions on large convex \(\ell\)-subgroups (Q2577771)

For an \(\ell\)-group \(G\), let \(C(G), L(G)\) and \(P(G)\) be the lattices of all convex \(\ell\)-subgroups, of all large convex \(\ell\)-subgroups and of all polar subgroups of \(G\), respectively. Further, let Spec\((G)\) be the root system of all prime subgroups of \(G\). From the author's introduction: ``In this paper, our main purpose is to study the atomic condition and the descending chain condition on the lattice \(L(G)\), while we also investigate some relations between the descending chain condition on \(L(G)\) and on \(C(G), P(G)\) and Spec\((G)\). As an application, we establish another characterization of Conrad's Finite Basis Theorem.''