# The Sym(3) Conjecture and Alt(8)

## TL;DR

This paper provides a new, computer-free proof that in the context of the Sym(3) conjecture, certain minimal counterexamples cannot have Soc(G)' isomorphic to Alt(8).

## Contribution

It offers an alternative proof avoiding computational methods for a key aspect of the Sym(3) conjecture.

## Key findings

- Minimal counterexamples' Soc(G)' cannot be isomorphic to Alt(8).
- Provides a computer-free proof of a known result.
- Strengthens understanding of the structure of potential counterexamples.

## Abstract

We give an alternate computer-free proof of a result of Z. Arad, M. Muzychuk, and A. Oliver: if G is a minimal counterexample to the Sym(3) conjecture, then Soc(G)' cannot be isomorphic to Alt(8).