OAI/GroupTheory/PolycyclicRecognition/Algebra/FiniteExponentLinearGroups.lean

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3 declarations, 0 contain sorry, 0 declared as axioms

Characteristic-zero matrix groups of finite exponent are finite

The irreducible case follows from finite trace coordinates. For a reducible action, induction applies to the actual subspace and quotient images, and the pair of images detects every element of finite order.

  1. theorem OAI.PolycyclicRecognition.PolynomialMatrixGroup.coordinateLinearAction_eq_implies_eq line 19
  2. theorem OAI.PolycyclicRecognition.PolynomialMatrixGroup.finite_of_faithful_common_exponent line 29
  3. theorem OAI.PolycyclicRecognition.PolynomialMatrixGroup.finite_of_faithful_common_exponent_charZero line 105