Theorems · Definition · group theory

MonoidHom.subgroupMap

{G : Type u_1} →
  {G' : Type u_2} →
    [inst : Group G] → [inst_1 : Group G'] → (f : G →* G') → (H : Subgroup G) → ↥H →* ↥(Subgroup.map f H)

The MonoidHom from a subgroup to its image.

Defined in: Mathlib.Algebra.Group.Subgroup.Map
Cited by: 8 results in Mathlib
Foundations: Depth 21 from the axioms · uses propext
Assumes: Group Group

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

Cites6

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

Groupstatement and proof · cited by 6,238
MonoidHomstatement and proof · cited by 3,629
Subgroupstatement and proof · cited by 3,593
Subgroup.mapstatement · cited by 301
Subgroup.toSubmonoidproof · cited by 114
MonoidHom.submonoidMapproof · cited by 4

Cited by8

Results whose statement or proof uses this declaration.

MonoidHom.subgroupMap_surjectivestatement · cited by 5
alternatingGroup.subgroup_eq_top_of_isPreprimitiveproof · cited by 1
isZGroup_of_coprimeproof · cited by 1
Subgroup.ker_subgroupMapstatement · cited by 1
Subgroup.card_map_dvdproof · cited by 0
IsZGroup.of_surjectiveproof · cited by 0
Subgroup.goursatproof · cited by 0
MonoidHom.subgroupMap_apply_coestatement and proof · cited by 0