Theorems · Definition · group theory
Subgroup.map
{G : Type u_1} → [inst : Group G] → {N : Type u_5} → [inst_1 : Group N] → (G →* N) → Subgroup G → Subgroup NThe image of a subgroup along a monoid homomorphism is a subgroup.
- Defined in
- Mathlib.Algebra.Group.Subgroup.Map
- Cited by
- 301 results in Mathlib
- Foundations
- Depth 20 from the axioms, rests on 110 definitions · uses propext
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- SetLike.coeproof · cited by 8,199
- Groupstatement and proof · cited by 6,238
- Set.imageproof · cited by 5,609
- MonoidHomstatement and proof · cited by 3,629
- Subgroupstatement and proof · cited by 3,593
- Submonoidproof · cited by 3,086
- Submonoid.mapproof · cited by 190
- Subgroup.toSubmonoidproof · cited by 114
Cited by330
Results whose statement or proof uses this declaration.
- MonoidHom.rangeproof · cited by 314
- MonoidHom.range_eq_mapstatement · cited by 37
- MonoidHom.map_closurestatement · cited by 16
- QuotientGroup.congrstatement and proof · cited by 16
- Subgroup.map_le_iff_le_comapstatement · cited by 13
- Subgroup.gc_map_comapstatement · cited by 12
- Subgroup.map_commutatorstatement and proof · cited by 12
- MulEquiv.mapSubgroupproof · cited by 11
- Subgroup.map_subtype_injstatement · cited by 11
- Subgroup.subgroupOf_map_subtypestatement · cited by 10
- Subgroup.map_botstatement · cited by 10
- Subgroup.comap_map_eqstatement and proof · cited by 9
Showing the 200 most cited of 330.