OAI/GroupTheory/PolycyclicRecognition/Geometry/BoundedDegreeRootsOfUnity.lean

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2 declarations, 0 contain sorry, 0 declared as axioms

Only finitely many roots of unity have bounded degree

The complex roots of the minimal polynomial are roots of the same equation X^m = 1. Its integral coefficients are uniformly bounded by the degree, so only finitely many minimal polynomials, and hence roots, can occur.

  1. theorem OAI.PolycyclicRecognition.torsion_minpoly_coeff_bound line 17
  2. theorem OAI.PolycyclicRecognition.finite_rootsOfUnity_of_bounded_degree line 41