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.

Key Words:

• Finite groups
• Saturated formations

Mathematical Subject Classification:

• 20D10
• 20F17

ACKNOWLEDGMENT

The research is supported by Proyecto BFM 2001-1667-C03-03, MCyT Spain and FEDER (European Union).

Notes

^#Communicated by A. Olshanskiy.