Composition and local critical formations (Q1603067)

The problem of the study of minimal local non-\(\mathfrak H\)-formations or, in other words, \({\mathfrak H}_1\)-critical formations was first posed by L. A. Shemetkov in 1980. This problem was investigated by several authors. This paper gives a description of the structure of \({\mathfrak H}_0\)-critical and \({\mathfrak H}_1\)-critical formations for an arbitrary composition or, respectively, local formation \(\mathfrak H\), which is a solution of L. A. Shemetkov's problem for the case of a local formation \(\mathfrak H\).