Finite groups whose 𝑛-maximal subgroups are subnormal

Introduction. Dedekind has determined all groups whose subgroups are all normal (see, e.g., [5, Theorem 12.5.4]). Partially generalizing this, Wielandt showed that afinite group is nilpotent, if and only if all its subgroups are subnormal, and also if and only if all maximal subgroups are normal [5, Corollary 10.3.1, 10.3.4]. Huppert [7, Satze 23, 24] has shown that if all 2nd-maximal subgroups of a finite group are normal, the group is...