Mathlib Map

Theorems · Theorem · group theory

Subgroup.subgroupOf_map_powMonoidHom_eq_range

∀ {M : Type u_6} [inst : CommGroup M] (S : Subgroup M) (n : ℕ),
  (Subgroup.map (powMonoidHom n) S).subgroupOf S = (powMonoidHom n).range
Defined in
Mathlib.Algebra.Group.Subgroup.Ker
Cited by
0 results in Mathlib
Foundations
Depth 26 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CommGroup
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Subgroup · cited by 3593SubgroupCommGroup · cited by 990CommGroupMonoidHom.range · cited by 314MonoidHom.rangeSubgroup.map · cited by 301Subgroup.mapSubgroup.subgroupOf · cited by 122Subgroup.subgroupOfSubgroup.ext · cited by 108Subgroup.extpow_mem · cited by 46pow_mempowMonoidHom · cited by 35powMonoidHompowMonoidHom_apply · cited by 11powMonoidHom_applySubgroup.subgroupOf_map_powMo…CITED BYCITES

Cites9

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by0

Results whose statement or proof uses this declaration.

Nothing cites this yet.