Soluble totally local formations (Q1921827)

The article is devoted to completing the description of soluble totally local formations and solution of Problem 12.72 from the Kourovka Notebook [12th ed. 1992; Zbl 0831.20003] which reads as follows: Let \(\mathfrak F\) be a soluble hereditary local formation. Prove that if every soluble minimal non-\(\mathfrak F\)-group \(G\) is a minimal non-\({\mathfrak N}^{l(G)-1}\)-group, then \(\mathfrak F\) is a totally local formation.