Fitting classes and lattice formations II

Abstract

Given a lattice formation & of full characteristic, an &-Fitting class is a Fitting class with stronger closure properties involving ^"-subnormal subgroups. The main aim of this paper is to prove that the associated injectors possess a good behaviour with respect to ^-subnormal subgroups.2000 Mathematics subject classification: primary 20D10.

Fitting classes and lattice formations I

“…Lattice formations and also the class of p-nilpotent groups, for every prime p, are particular examples of the formations # considered in Theorem 3.9. In particular, this theorem and Proposition 3.4 (a) improve Theorem 2.8, parts (1) and (2).…”

“…In this manner, notice that an ^"-Fitting class is also a Fitting class, as the lattice formation J*" contains jV. In a forthcoming paper [2], the desired behaviour of the associated injectors, with respect to ^"-subnormal (and ^"-Dnormal) subgroups, is obtained. In fact, this property characterizes ^"-Fitting classes.…”

“…This lattice contains the set of all "-Dnormal subgroups as a sublattice. 94 M. Arroyo-Jorda and M. D. Perez-Ramos [2] In fact, the lattice properties of ^"-subnormal subgroups, and also the lattice properties of ^-Dnormal subgroups, characterize the lattice formations among all the subgroup-closed saturated formations &'. (See Theorem 2.7.…”