The lattice of formations with the Shemetkov property
A. Ballester‐Bolinches, Sergey Fedorovich Kamornikov, X. Yi · Journal of Algebra and Its Applications · 2024
Let [Formula: see text] be a class of finite groups. A group [Formula: see text] is called a minimal non-[Formula: see text]-group or simply an [Formula: see text]-critical group, if [Formula: see text] is not in [Formula: see text] but all proper subgroups of [Formula: see text] are in [Formula: see text]. An [Formula: see text]-critical group, for the class [Formula: see text] all finite nilpotent groups, is called a Schmidt group. We say that a formation [Formula: see text] has the Shemetkov property if every [Formula: see text]-critical group is either a Schmidt group or a cyclic group of prime order. In this paper, properties of the lattice of all soluble subgroup-closed local formations with Shemetkov property are investigated.