There is no Sz(8) in the Monster

TL;DR

This paper proves that the Suzuki group Sz(8) does not exist as a subgroup within the Monster group, advancing the understanding of the Monster's subgroup structure with minimal reliance on computer assistance.

Contribution

It provides a largely computer-free proof that Sz(8) is not a subgroup of the Monster, contributing to the classification of the Monster's maximal subgroups.

Findings

Sz(8) is not a subgroup of the Monster

The proof reduces reliance on computational methods

Advances the classification of the Monster's subgroups

Abstract

As a contribution to an eventual solution of the problem of the determination of the maximal subgroups of the Monster we show that there is no subgroup isomorphic to Sz(8). The proof is largely, though not entirely, computer-free.