Finite groups with $\Bbb P$-subnormal 2-maximal subgroups

Abstract

A subgroup $H$ of a group $G$ is called $\Bbb P$-{\sl subnormal} in $G$ if either $H=G$ or there is a chain of subgroups $H=H_0\subset H_1\subset...\subset H_n=G$ such that $|H_i:H_{i-1}|$ is prime for $1\le i\le n$. In this paper we study the groups all of whose 2-maximal subgroups are $\Bbb P$-subnormal.