ON 𝔛-SATURATED FORMATIONS OF FINITE GROUPS

ABSTRACT

In the paper, a Frattini-like subgroup associated with a class 𝔛 of simple groups is introduced and analyzed. The corresponding 𝔛-saturated formations are exactly the 𝔛-local ones introduced by Förster. Our techniques are also useful to highlight the properties and behavior of ω-local formations. In fact, extensions and improvements of several results of Shemetkov are natural consequences of our study.