In this chapter we solve the main conjugacy problems for unipotent elements of symplectic and orthogonal groups in characteristic 2. Many of the methods of Chapter 4 do not apply: there is no Cayley map between unipotent and nilpotent elements, nor is there a factorization of the centralizer of a unipotent element in a canonical parabolic subgroup. Hence, although we can exploit some features of the good characteristic case, our algorithms are more complicated.

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Unipotent Classes in Bad Characteristic

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

摘要

In this chapter we solve the main conjugacy problems for unipotent elements of symplectic and orthogonal groups in characteristic 2. Many of the methods of Chapter 4 do not apply: there is no Cayley map between unipotent and nilpotent elements, nor is there a factorization of the centralizer of a unipotent element in a canonical parabolic subgroup. Hence, although we can exploit some features of the good characteristic case, our algorithms are more complicated.