  Let $G$ be a finite group and $\sigma=\{\sigma_{i}|i\in I\}$ be a partition
of the set of all primes $\mathbb{P}$, that is, $\mathbb{P}=\bigcup_{i\in
I}\sigma_{i}$ and $\sigma_{i}\cap \sigma_{j}=\emptyset$ for all $i\neq j$. A
chief factor $H/K$ of $G$ is said to be $\sigma$-central in $G$, if the
semidirect product $(H/K)\rtimes(G/C_G(H/K))$ is a $\sigma_i$-group for some
$i\in I$. The group $G$ is said to be $\sigma$-nilpotent if either $G=1$ or
every chief factor of $G$ is $\sigma$-central. In this paper, we study the
properties of a finite group $G=AB$, factorized by two $\sigma$-nilpotent
subgroups $A$ and $B$, and also generalize some known results.
