  A subgroup $H$ of a group $G$ is called $\mathbb P$-subnormal in $G$ whenever
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 a prime for all $i$. In this paper,
we study the groups in which all primary cyclic subgroups are $\mathbb
P$-subnormal.
