Subdirect products and formations of finite groups (Q1814495)

A constructive description of finite subdirect products of finite or infinite groups is obtained. It uses for description the structure of the subgroups of a direct product of groups in terms of the subgroups of the direct factors when the number of factors is finite. The results obtained are used for the solution of a problem of Shemetkov concerning the enumeration of formations of finite groups in which all subformations are \(s_ n\)-closed. For the solution of Shemetkov's problem a new class of finite groups is constructed.