Throughout this paper, all groups are finite. Let $sigma ={sigma_{i} | iin I }$ be some partition of the set of all primes $Bbb{P}$. If $n$ is an integer, the symbol $sigma (n)$ denotes the set ${sigma_{i} |sigma_{i}cap pi (n) e emptyset }$. The integers $n$ and $m$ are called $sigma$-coprime if $sigma (n)cap sigma (m)=emptyset$. Let $t > 1$ be a natural number and let $mathfrak{F}$ be a class of groups. Then we say that $mathfrak{F}$ is $Sigma_{t}^{sigma}$-closed provided $mathfrak{F}$ contains each group $G$ with subgroups $A_{1}, ldots , A_{t}in mathfrak{F}$ whose indices $|G:A_{1}|$, $ldots$, $|G:A_{t}|$ are pairwise $sigma$-coprime. In this paper, we study $Sigma_{t}^{sigma}$-closed classes of finite groups.
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