ON LATTICES OF RADICALS IN THE CLASS OF ALL FINITE GROUPS

Abstract

AbstractLattices of radicals have been extensively studied, for example in the class of associative rings, leading to some interesting results. In this paper we investigate the lattice L of all radicals in the class of all finite groups. We also consider some of its important sublattices. In particular, we prove that the lattice L is closed to being modular, the lattice Lh of all hereditary radicals is a Boolean algebra, and there exists a natural, useful projection of the lattice L onto Lh.