Laws of the lattice of all $${\mathfrak {X}}$$-local formations of finite groups

Abstract

Let $${\mathfrak {X}}$$ be a class of simple groups with a completeness property $$\pi ({\mathfrak {X}}) = \mathrm {char} \, {\mathfrak {X}}$$ . A formation is a class of finite groups closed under taking homomorphic images and finite subdirect products. Forster introduced the concept of $${\mathfrak {X}}$$ -local formation in order to obtain a common extension of well-known Gaschutz–Lubeseder–Schmid, and Baer theorems (Publ Mat Univ Autonoma Barcelona 29(2–3):39–76, 1985). In the present paper, it is shown that any law of the lattice of all formations is true in the lattice of all $${\mathfrak {X}}$$ -local formations.