Linear groups whose proper subgroups are close to being nilpotent

The aim of this paper is to describe linear groups in which all proper subgroups belong to a group class (Formula presented.) for several relevant choices of (Formula presented.) In particular, we study linear groups either with only nilpotent-by-finite proper subgroups or with only paranilpotent subgroups; here a group G is paranilpotent if it has a normal series of finite length whose factors are abelian and have only G-invariant subgroups.