OAI/GroupTheory/PolycyclicRecognition/Algebra/RationalNilpotentRank.lean

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Nilpotent rational rank from a homology bound

Finite-index torsion-free subgroups of finitely generated nilpotent groups have a top orientation class. Detecting this class after rationalization bounds every lattice quotient. Lifting finite independent families then bounds abelian quotients of arbitrary nilpotent groups, including torsion.

  1. theorem OAI.PolycyclicRecognition.finitelyGenerated_nilpotent_lattice_quotient_rank_le_of_rational_bound line 19
  2. theorem OAI.PolycyclicRecognition.nilpotent_abelian_quotient_lattice_rank_le_of_rational_bound line 51
  3. theorem OAI.PolycyclicRecognition.nilpotent_abelian_quotient_rank_le_of_rational_bound line 74
  4. theorem OAI.PolycyclicRecognition.nilpotent_rational_abelianization_finite_of_homology_bound line 87
  5. theorem OAI.PolycyclicRecognition.nilpotent_rational_abelianization_finite_iff_homology_bounded line 96