On \({\mathfrak F}\)-critical groups
We say that a saturated formation \(\mathcal F\) has the Shemetkov property if every \(\mathcal F\)-critical group is either a Shmidt group or a cyclic group of prime order. The paper gives an exact description of the subgroup- closed saturated formations of soluble groups \(\mathcal F\) for which the Shemetkov property holds. With respect to the non-soluble case, the authors determine a necessary condition for a subgroup-closed saturated formation \(\mathcal F\) to have the Shemetkov property. Examples of subgroup- closed saturated formations with the Shemetkov property of a different nature are given.
scientific article; zbMATH DE number 783898