Nonabelian composition factors of finite groups whose maximal subgroups are complemented: A solution to Kourovka Problem 18.68

Abstract

Status: This preprint claims a complete CFSG-conditional solution to Kourovka Problem 18.68, but it has not yet been externally refereed or established by publication. It proves that the possible nonabelian composition factors of a finite group whose maximal subgroups are complemented are precisely PSL(2,7), PSL(2,11), and PSL(5,2). The arbitrary direct-power case is handled by a primitive product-action reduction, and the last infinite factor-screen survivor is eliminated by a uniform 2-adic obstruction. The deposit contains the 11-page manuscript, a complete source-and-certificate archive, and SHA-256 checksums. The archive includes the internal proof audit, GAP 4.15.1/Table-of-Marks producers, pinned TomLib 1.2.11 certificates, independent Python checkers, and deterministic build instructions. A clean release check reproduced all certificates and the PDF. AI agents were used extensively for literature search, proof exploration, code generation, drafting, and adversarial review. The author selected the arguments and sources, reran the reported computations, and assumes full responsibility for all claims and citations.