Richie Sater

Generation of finite groups from subgroups of coprime index

Version 1.1.3 of the preprint and its supporting source records answer Kourovka Notebook Problem 21.87. Let d(G) be the least size of a generating set of a finite group G. If G has a nonempty family of subgroups, each generated by at most d elements, whose indices have greatest c...

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)),...

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...

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...