On m-$$\sigma$$-embedded subgroups of finite groups

Let $$\sigma =\{\sigma_i |i\in I\}$$ be some partition of the set of all primes $$\mathbb{P}$$ and G be a finite group. A group is said to be $$\sigma$$ -primary if it is a finite $$\sigma_{i}$$ -group for some i. A subgroup A of G is said to be $${\sigma}$$ -subnormal in G if there is a subgroup chain $$A=A_{0} \leq A_{1} \leq \cdots \leq A_{t}=G$$ such that either $$A_{i-1}\trianglelefteq A_{i}$$ or $$A_{i}/(A_{i-1})_{A_{i}}$$ is $$\sigma$$ -primary for all $$i=1, \ldots , t$$ . A subgroup S of G is m- $$\sigma$$ -permutable in G if $$S=\langle M, B \rangle$$ for some modular subgroup M and $$\sigma$$ -permutable subgroup B of G. We say that a subgroup H of G is m- $$\sigma$$ -embedded in G if there exist an m- $$\sigma$$ -permutable subgroup S and a $$\sigma$$ -subnormal subgroup T of G such that $$H^G=HT$$ and $$H\cap T\leq S\leq H$$ , where $$H^G = \langle H^x | x \in G \rangle$$ is the normal closure of H in G. In this paper, we study the properties of m- $$\sigma$$ -embedded subgroups and use them to determine the structure of finite groups. Some known results are generalized.