quotientCenterEmbedding — Mathlib

English

Assuming a free and transitive action, there is an equivalence between orbits of H on β and the quotient α/H.

Русский

При свободном и транзитивном действии существует эквивалентность орбит H на β и фактор-группа α/H.

LaTeX

$$equivSubgroupOrbitsQuotientGroup$$

Lean4

/-- If `G` is generated by `S`, then the quotient by the center embeds into `S`-indexed sequences
of commutators. -/
noncomputable def quotientCenterEmbedding {S : Set G} (hS : closure S = ⊤) : G ⧸ center G ↪ S → commutatorSet G :=
  (quotientEquivOfEq (center_eq_infi' S hS)).toEmbedding.trans
    ((quotientiInfEmbedding _).trans (Function.Embedding.piCongrRight fun g => quotientCentralizerEmbedding (g : G)))

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