Direct decompositions of τ-closed n-multiply ⍵-composition formations
Let {𝔉i | i ∈ I} be a system of non-empty formations such that 𝜋(𝔉i) ∩ 𝜋(𝔉j) = ∅ for all distinct i, j ∈ I. Let = ⊗i∈I𝔉i be a class of groups А1 × А2 ×... × Аt, where А1∈ 𝔉i1, А2∈ 𝔉i2,..., Аt ∈ 𝔉it for some i1, i2,..., it ∈ I. It is proved that the formation is a τ-closed n-multiply ⍵-composition if and only if every formation 𝔉i is a τ-closed n-multiply ⍵-composition.