OAI/GroupTheory/PolycyclicRecognition/Algebra/NilpotentAscendingBase.lean

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3 declarations, 0 contain sorry, 0 declared as axioms

Ascending bases lift from a nilpotent abelianization

This proves the lifting step used in Kropholler--Martínez-Pérez--Nucinkis, J. reine angew. Math. 637 (2009), Lemma 2.3. The last lower-central subgroup is central. Commutators of quotient lifts give its stable finite base, and finite lift errors are absorbed before continuing by induction.

  1. theorem OAI.PolycyclicRecognition.ascending_base_of_commutator_eq_bot line 17
  2. theorem OAI.PolycyclicRecognition.nilpotent_ascending_base_induction line 29
  3. theorem OAI.PolycyclicRecognition.nilpotent_ascending_base_of_abelianization line 58