A New Approach from Lattice of Subgroup Sets to Generalized Solvable Extension Formations

In this paper, we establish the decomposition of morphisms from lattice of subgroup sets to generalized solvable extension formations. To achieve this, we develop a unified framework involving maximal subgroup functors, generating formation morphism and contraction-extension functors. In particular, solvability-induced sets of maximal subgroups are determined and generating formation morphism gives rise to generalized solvable extension formations.