Groups satisfying the maximal condition on non-ascendant subgroups. (Q2568770)

The author studies groups satisfying the maximal condition on non-ascendant subgroups. The main results of the article are the following: Let \(G\) be an infinite group. Then every subgroup of infinite index is ascendant in \(G\) iff G is either an \(N\)-group or \(G\) is a semidirect product of a normal finite nilpotent and infinite cyclic subgroups. A soluble locally nilpotent group satisfying the maximal condition on non-ascendant subgroups is an \(N\)-group. An infinite locally finite group satisfying the maximal condition on non-ascendant subgroups is a Gruenberg group.