Finite simple groups with narrow prime spectrum

TL;DR

This paper classifies nonabelian finite simple groups with prime divisors of their order not exceeding 1000, providing a detailed analysis of their prime spectra using computational methods.

Contribution

It identifies and characterizes all nonabelian finite simple groups with maximal prime divisors below 1000, extending previous classifications.

Findings

List of nonabelian finite simple groups with prime divisors ≤ 1000

Determination of groups with a fixed maximal prime divisor less than 1000

Use of GAP for computational verification

Abstract

We find the nonabelian finite simple groups with order prime divisors not exceeding 1000. More generally, we determine the sets of nonabelian finite simple groups whose maximal order prime divisor is a fixed prime less than 1000. Our results are based on calculations in the computer algebra system GAP.