The Quantitative Characterization of Finite Simple Groups

TL;DR

This paper presents a uniform method to characterize all finite simple groups solely based on their order and the set of element orders, simplifying their classification.

Contribution

It introduces a novel approach to identify finite simple groups using only their order and element order set, streamlining classification.

Findings

Finite simple groups can be characterized by their order and element orders

A uniform method for identifying finite simple groups is established

Simplifies the classification process for finite simple groups

Abstract

In this report we summarize this work, all finite simple groups $G$ can determined uniformly using their orders $|G|$ and the set $\pi_e(G)$ of their element orders.