Quantitative characterization of finite simple groups: a complement

TL;DR

This paper reviews the characterization of finite simple groups based on element orders, discusses related topics and applications, and highlights its relevance in mathematics and computational complexity theory.

Contribution

It provides a comprehensive summary and expansion of existing work on finite simple groups and their element order characterizations, including new applications and generalizations.

Findings

Characterization of finite simple groups based on element orders

Applications in mathematics and computational complexity

Corrections and expansions of previous work

Abstract

In this paper, we summarize the work on the characterization of finite simple groups and the study on finite groups with the set of element orders and two orders (the order of group and the set of element orders). Some related topics, and the applications together with their generalizations are also discussed. The original version of this article was published in Chinese in the journal Scientia Sinica Mathematica, no.53(2023), pp.931-952. This revised and expanded version has corrected several errors and added quite a few contents. Especially, it is pointed that this work has applications in mathematics and computational complexity theory.