Finite groups with given generalized maximal subgroups (Review). I. Finite group with generalized normal $n$-maximal subgroup

Let $G$ be a finite group. A chain of subgroups $H_n<H_{n-1}<\dots<H_1<H_0=G$ of $G$ such that $H_i$ is a maximal subgroup of $H_{i-1}$ for every $i=1,\dots,n$ is called a maximal chain of length $n$. A subgroup $H$ of $G$ is said to be an $n$-maximal subgroup of $G$ if $H$ is the latest member of some maximal chain of $G$ of length $n$. In this review, we give the analisis of the most famous papers in which finite groups with generalized normal $n$-maximal subgroups are developed.