On $Σ_t^{σ}$ -closed classes of finite groups - Skiba, A. N.; Zhang, Chi (Ukrains’kyi Matematychnyi Zhurnal, 2018)
All analyzed groups are finite. Let $σ = \{ σ_i| i \in I\}$ be a partition of the set of all primes $\mathbb{P}$. If $n$ is an integer, then thesymbol $σ (n)$ denotes a set $\{σ_i| σ_i \cap π (n) ot = \emptyset\}$. Integers $n$ and $m$ are called $σ$ -coprime if $σ (n) \cap σ (m) = \emptyset$. Let $t > 1$ be a natural number and let $\mathfrak{F}$ be a class of groups. Then we say that $\mathfrak{F}$ is $Σ^{σ}_ t$ -closed provided $\mathfrak{F}$ contains each group $G$ with subgroups $A_1, ... ,A_t \in \mathfrak{F}$ whose indices $| G : A_1| ,..., | G : A_t|$ are pairwise $σ$ -coprime.We study $Σ_t^{σ}$ -closed classes of finite groups.