Injectors of finite $\sigma$-soluble groups

Let $\sigma=\{\sigma_i: i\in I\}$ be some partition of the set of all primes $\mathbb{P}$, i. e. $\mathbb{P}=\cup_{i\in I}\sigma_i$ and $\sigma_i\cap\sigma_j=\varnothing$ for all $i\ne j$. Finite group $G$ is $\sigma$-soluble, if every chief factor $H/K$ of $G$ is a $\sigma_i$-group for some $\sigma_i\in\sigma$. Fitting class $\mathfrak{H}=\cap_{\sigma_i\in\sigma}h(\sigma_i)\mathfrak{E}_{\sigma_i'}\mathfrak{E}_{\sigma_i}$ is said to be $\sigma$-class Hartley. In this paper we prove the existence and conjugacy of $\mathfrak{H}$-injectors of $G$ and describe their characterization in the terminal of the radicals.