Expressing the statement of the Feit-Thompson theorem with diagrams in the category of finite groups

TL;DR

This paper reformulates the Feit-Thompson theorem using diagrammatic language in the category of finite groups, employing Quillen lifting properties to provide a new categorical perspective.

Contribution

It introduces a novel diagrammatic formulation of the Feit-Thompson theorem within finite group categories, connecting group theory with categorical diagram techniques.

Findings

Reformulation of the Feit-Thompson theorem using diagrams

Application of Quillen lifting properties in finite groups

New categorical perspective on group-theoretic theorems

Abstract

We reformulate the statement of the Feit-Thompson theorem in terms of diagrams in the category of finite groups, namely iterations of the Quillen lifting property with respect to particular morphisms.