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This book is a study of conjugacy in finite classical groups: the general and special linear, symplectic, orthogonal and unitary groups over finite fields. In this chapter we introduce the three main conjugacy problems studied. First we describe the problems and some of their history. Then we present both our strategy to solve them and a summary of our main results. Finally, we discuss our related algorithms and their performance, and the role they play in the solution of these problems for arbitrary finite groups.

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Introduction and Background

  • 章节

  • 发表日期：

    2025年

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  • Giovanni De Franceschi,
  • Martin W. Liebeck,
  • Eamonn A. O’Brien

摘要

This book is a study of conjugacy in finite classical groups: the general and special linear, symplectic, orthogonal and unitary groups over finite fields. In this chapter we introduce the three main conjugacy problems studied. First we describe the problems and some of their history. Then we present both our strategy to solve them and a summary of our main results. Finally, we discuss our related algorithms and their performance, and the role they play in the solution of these problems for arbitrary finite groups.