Richie Sater

Generation of finite groups from subgroups of coprime index

Peer-review preprint and complete proof-audit trail for a claimed affirmative solution of Kourovka Notebook Problem 21.87. The manuscript proves, modulo the published inputs identified in the paper, that Lucchini's general generator bound sharpens from d+2 to d+1 for a finite gro...

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

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 complem...

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

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)),...

A Stabilizer Obstruction for Anonymous and Object-Neutral Classification Aggregation

We disprove a conjectured prime-divisor characterization for anonymous and object-neutral classification aggregation. A general stabilizer obstruction and explicit profile gadgets show that, for every m ≥ 5, ρ = m − 2, and n ≥ 2, no deterministic resolute anonymous and object-neu...