Finite Groups with $$\sigma $$-Subnormal Schmidt Subgroups

Abstract If $$\sigma = \{ {\sigma }_{i} : i \in I \}$$ σ = { i : ∈ I } is a partition of the set $$\mathbb {P}$$ P all prime numbers, subgroup H finite group G said to be $$ - subnormal in if can joined by means chain subgroups $$H=H_{0} \subseteq H_{1} \cdots H_{n}=G$$ H 0 ⊆ 1 ⋯ n G such that either $$H_{i-1}$$ - normal $$H_{i}$$ or $$H_{i}/{{\,\mathrm{Core}\,}}_{H_{i}}(H_{i-1})$$ / Core ( ) $${\sigma }_{j}$$ j -group for some $$j I$$ , every $$i=1, \ldots n$$ , … . \{\{2\}, \{3\}, \{5\}, ... 2 3 5 . minimal partition, then -subnormality reduces classical embedding property subnormality. A X Schmidt not nilpotent and proper nilpotent. Every non-nilpotent has detailed knowledge their provide deep insight into its structure. In this paper, complete description with -subnormal given. It answers question posed Guo, Safonova Skiba.