Groups with nearly modular subgroup lattice (Q2717701)

A subgroup \(H\) of a group \(G\) is called nearly modular in \(G\) if \(H\) has finite index in a modular element of the lattice of subgroups of \(G\). The authors study groups in which every subgroup is nearly modular. They show that the set \(T\) of elements of finite order in such a group \(G\) is a subgroup of \(G\). If \(G\) is locally graded (that is, every nontrivial finitely generated subgroup of \(G\) has a proper subgroup of finite index), then \(T\) is locally finite and \(G/T\) is Abelian; if \(G\neq T\), then every subgroup of \(T\) is nearly normal in \(G\), and either \(G\) is an FC-group or \(G/T\) is torsionfree of rank 1.