The time complexity of some algorithms for generating the spectra of finite simple groups

TL;DR

This paper investigates the computational complexity involved in generating the spectrum of finite simple groups, focusing on different classes such as alternating and Lie type groups, based on their defining parameters.

Contribution

It analyzes the time complexity of algorithms for computing the spectra of finite simple groups given their structural parameters.

Findings

Provides complexity bounds for spectrum generation algorithms

Identifies efficient methods for specific classes of finite simple groups

Highlights computational challenges in spectrum determination

Abstract

The spectrum $\omega(G)$ is the set of orders of elements of $G$. We consider the problem of generating the spectrum of a finite nonabelian simple group $G$ given by the degree of $G$ if $G$ is an alternating group, or the Lie type, Lie rank and order of the underlying field if $G$ is a group of Lie type.