Direct decompositions of τ-closed n-multiply ⍵-composition formations
Let {𝔉<sub>i</sub> | i ∈ I} be a system of non-empty formations such that 𝜋(𝔉<sub>i</sub>) ∩ 𝜋(𝔉<sub>j</sub>) = ∅ for all distinct i, j ∈ I. Let = ⊗<sub>i∈I</sub>𝔉<sub>i</sub> be a class of groups А<sub>1</sub> × А<sub>2</sub> ×... × А<sub>t</sub>, where А<sub>1</sub>∈ 𝔉<sub>i</sub><sub>1</sub>, А<sub>2</sub>∈ 𝔉<sub>i</sub><sub>2</sub>,..., А<sub>t</sub> ∈ 𝔉<sub>i</sub><sub>t</sub> for some i<sub>1</sub>, i<sub>2</sub>,..., i<sub>t</sub> ∈ I. It is proved that the formation is a τ-closed n-multiply ⍵-composition if and only if every formation 𝔉<sub>i</sub> is a τ-closed n-multiply ⍵-composition.