OAI/GroupTheory/PolycyclicRecognition/Algebra/FiniteTorsionPowerSubgroup.lean

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5 declarations, 0 contain sorry, 0 declared as axioms

A characteristic torsion-free subgroup of finite index in an abelian group

When the torsion subgroup is finite, its order annihilates it. The subgroup of that power is torsion-free, and finite reduction gives its finite index.

  1. def OAI.PolycyclicRecognition.abelianPowerReduction line 17
  2. theorem OAI.PolycyclicRecognition.abelianPowerReduction_ker line 24
  3. theorem OAI.PolycyclicRecognition.abelianPowerRange_characteristic line 39
  4. theorem OAI.PolycyclicRecognition.abelianPowerRange_finiteIndex line 48
  5. theorem OAI.PolycyclicRecognition.abelianPowerRange_torsionFree line 54