The semisimple conjugacy classes in the symplectic groups

TL;DR

This paper classifies the conjugacy classes of semisimple elements in symplectic groups over arbitrary fields of characteristic not 2, providing a detailed algebraic understanding of their structure.

Contribution

It explicitly determines the semisimple conjugacy classes in symplectic groups over any field with characteristic not 2, extending previous classifications.

Findings

Complete classification of semisimple conjugacy classes in Sp(2m, F)

Applicable to fields of any characteristic not 2

Provides foundational results for further algebraic studies

Abstract

We determine the conjugacy classes of semisimple elements in the symplectic groups ${\rm Sp}(2m,F)$, where $F$ is an arbitrary field of characteristic not $2$. This note was originally a letter dated 23 March, 2006, from G.E. Wall to Cheryl E. Praeger, and has been reproduced with his kind permission.