OAI/GroupTheory/PolycyclicRecognition/Algebra/CentralFiltrationAction.lean

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3 declarations, 0 contain sorry, 0 declared as axioms

Nilpotence detected by an action on a central filtration

The three subgroups lemma increases the depth of a commutator action. Once the lower central series centralizes the last filtration term, a centralizer bound puts it inside that term; the action then lowers it to the identity.

  1. theorem OAI.PolycyclicRecognition.commutator_commutator_le_of_rotate line 17
  2. theorem OAI.PolycyclicRecognition.lowerCentralSeries_action_depth line 29
  3. theorem OAI.PolycyclicRecognition.nilpotent_of_central_filtration_action line 52