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

Abstract

IMPORTANT CORRECTION — VERSION 1.0.2: This version supersedes versions 1.0.0 and 1.0.1, which contained an acceptance-level proof gap in the graph-outer PSp(4,4) case. Those versions are preserved for provenance but must not be cited as the complete proof. For X = Aut(PSp(4,4)), the former orthogonal-normalizer action had degree 272 and did not supplement the socle. Version 1.0.2 withdraws that construction. It uses a prime-degree subfield action of degree 1360 at q = 4 and proves a uniform 2-adic obstruction for every field-only or graph-outer coordinate group and every socle multiplicity. Status: This preprint claims a complete CFSG-conditional solution to Kourovka Problem 18.68. Four internal adversarial review rounds passed and recommend circulation, but no independent external finite-group specialist has yet reviewed it. The claimed nonabelian composition factors are precisely PSL(2,7), PSL(2,11), and PSL(5,2). The deposit contains the corrected 12-page manuscript, complete internal review trail, source archive, SHA-256 manifest, GAP 4.15.1/TomLib 1.2.11/AtlasRep 2.1.11 certificates, independent Python checkers, seven mutation controls, and deterministic build receipt. AI tools were used extensively for literature search, proof exploration, code generation, drafting, and adversarial review. Richie Sater is the sole author and assumes full responsibility for every claim, source, computation, and release.