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In this chapter we use the results in the semisimple and unipotent cases to solve the main conjugacy problems for classical groups: list representatives for all conjugacy classes; describe the structure of the centralizer of an arbitrary element and provide a generating set; decide conjugacy between arbitrary elements and construct explicit conjugating elements.

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General Conjugacy Classes

  • 章节

  • 发表日期：

    2025年

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

摘要

In this chapter we use the results in the semisimple and unipotent cases to solve the main conjugacy problems for classical groups: list representatives for all conjugacy classes; describe the structure of the centralizer of an arbitrary element and provide a generating set; decide conjugacy between arbitrary elements and construct explicit conjugating elements.