On one generalization of finite $\mathfrak{U}$-critical groups

Abstract

A proper subgroup $H$ of a group $G$ is said to be: $\mathbb{P}$-subnormal in $G$ if there exists a chain of subgroups $H=H_0<H_1<...<H_n=G$ such that $|H_i:H_{i-1}|$ is a prime for $i=1,...,n$; $\mathbb{P}$-abnormal in $G$ if for every two subgroups $K\le L$ of $G$, where $H\le K$, $|L:K|$ is not a prime. In this paper we describe finite groups in which every non-identity subgroup is either $\mathbb{P}$-subnormal or $\mathbb{P}$-abnormal.