Finite groups with \(f\)-abnormal or \(f\)-subnormal subgroups (Q1898516)

A formation \(f\) is said to be an \(\check S\)-formation if each finite solvable minimal non-\(f\)-group is either a Shmidt group or a group of prime order. The paper contains a new characterization of solvable local hereditary \(\check S\)-formations. One proves that a hereditary local solvable formation \(f\) is an \(\check S\)-formation if and only if \(f\) contains each group \(G=AB\), where \(A\) and \(B\) are \(f\)-subnormal \(f\)- subgroups of the group \(G\). Making use of this result, the author obtains a description of finite groups for which any proper subgroup is either \(f\)-subnormal or \(f\)-abnormal for an arbitrary hereditary solvable \(\check S\)-formation.