The maximum order of the elements of a finite symplectic group of even characteristic

TL;DR

This paper derives an exact formula for the maximum order of elements in finite symplectic groups of even characteristic and their automorphism groups, based on parameters m and q.

Contribution

It provides a precise formula for element orders in symplectic groups over fields of even characteristic, extending understanding of their structure.

Findings

Exact formula for maximum element order in Sp(2m,q) with q even

Formula also applies to automorphism groups of these symplectic groups

Enhances knowledge of element structure in symplectic groups of even characteristic

Abstract

We give an exact formula, as a function of m and q, for the maximum order of the elements of the finite symplectic group Sp(2m,q), with q even, and of its automorphism group.