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Mikhail Borovoi
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A reference: Steinberg, Torsion in reductive groups, Advances in Math. 15 (1975), 63–92, Corollary 3.11.

In positive characteristic: loc. cit, Theorem 3.14.

See also: Connectedness of centralizers of semisimple Lie-algebra elements under the action of a semisimple algebraic group

Mikhail Borovoi
  • 14.2k
  • 2
  • 32
  • 72