Spectra of finite symplectic and orthogonal groups

TL;DR

This paper provides an arithmetic description of the spectra, i.e., element orders, of finite symplectic and orthogonal groups, including all finite simple cases, enhancing understanding of their algebraic structure.

Contribution

It offers a comprehensive arithmetic characterization of spectra for finite symplectic and orthogonal groups, including simple groups, which was previously not fully described.

Findings

Complete spectra descriptions for all finite simple symplectic groups.

Complete spectra descriptions for all finite simple orthogonal groups.

Enhanced understanding of element order structures in these classical groups.

Abstract

The spectra of a finite group is the set of its element orders. We obtain an arithmetic description of finite symplectic and orthogonal groups. In particular, a description of spectra of all finite simple simplectic and orthogonal groups is obtained.