OAI/GroupTheory/PolycyclicRecognition/Algebra/FiniteOrbitContractor.lean

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7 declarations, 0 contain sorry, 0 declared as axioms

A contractor fixed by a finite group

Products of commuting ascending actions retain an ascending base. Consequently the product of a finite orbit of contracting elements is invariant and remains contracting. This is the finite conjugation step in KMN, Lemma 2.2; no assertion that an FP-infinity group supplies an initial contractor is made here.

  1. theorem OAI.PolycyclicRecognition.ascendingBase_finite_product line 18
  2. def OAI.PolycyclicRecognition.finiteOrbitProduct line 32
  3. theorem OAI.PolycyclicRecognition.finiteOrbitProduct_fixed line 34
  4. theorem OAI.PolycyclicRecognition.finiteOrbitProduct_ascendingBase line 43
  5. theorem OAI.PolycyclicRecognition.finiteOrbitProduct_central line 50
  6. theorem OAI.PolycyclicRecognition.HasFinitelyGeneratedAscendingBase.conj line 60
  7. theorem OAI.PolycyclicRecognition.finiteOrbitProduct_ascendingBase_of_conjugate line 68