On groups with many nearly maximal subgroups
A subgroup \(M\) of a group \(G\) is said to be nearly maximal if it has infinite index but every larger subgroup has finite index in \(G\). Now groups in which every subgroup is an intersection of maximal subgroups have been studied by several authors and are called IM-groups. Here the authors consider groups in which every subgroup of infinite index is an intersection of nearly maximal subgroups, under the name nearly IM-groups. They prove that if \(G\) is an infinite hyper-(abelian or finite) group, then \(G\) is nearly IM if and only if \(G\) is cyclic or dihedral.
scientific article; zbMATH DE number 1281972
scientific article