OAI/GroupTheory/PolycyclicRecognition/Algebra/LocallyNilpotentDimension.lean

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6 declarations, 0 contain sorry, 0 declared as axioms

Finite integral dimension makes local nilpotence uniform

Every element of a lower-central term is witnessed in a finitely generated subgroup. The common class bound from cohomological dimension therefore makes a locally nilpotent group nilpotent, including groups not finitely generated.

  1. def OAI.PolycyclicRecognition.fgLowerCentralSubgroup line 20
  2. theorem OAI.PolycyclicRecognition.lowerCentralSeries_le_fgLowerCentral line 32
  3. theorem OAI.PolycyclicRecognition.lowerCentralSeries_eq_bot_of_fg_subgroups line 54
  4. theorem OAI.PolycyclicRecognition.locallyNilpotent_lowerCentralSeries_bound line 62
  5. theorem OAI.PolycyclicRecognition.HasFiniteIntegralCohomologicalDimension.nilpotent_of_locallyNilpotent line 73
  6. theorem OAI.PolycyclicRecognition.IsIntegralPoincareDualityGroup.polycyclic_of_locallyNilpotent line 82