Remarks on formations
The paper deals with some questions concerning the theory of formations of finite groups by applying the normalizer theory of finite groups developed in 1989. A description of local formations with a unique maximal local definition, generalizing Doerk's one in the soluble case, and a description of local formations \({\mathcal F}\) such that the unique largest subgroup-closed class contained in \({\mathcal F}\) is also a local formation are given. Then, one studies the formation generated by a finite group \(G\) in terms of the formation generated by quotients of \(G\). Finally, the Schunck classes which are saturated formations are characterized by means of a property of their boundaries.
scientific article; zbMATH DE number 21528
scientific article