Theorems · Theorem · group theory
Subgroup.IsSubnormal.map
∀ {G : Type u_1} [inst : Group G] {H : Subgroup G} {G' : Type u_2} [inst_1 : Group G'] {f : G →* G'},
Function.Surjective ⇑f → H.IsSubnormal → (Subgroup.map f H).IsSubnormalThe image of a subnormal subgroup under a surjective homomorphism is subnormal.
- Defined in
- Mathlib.GroupTheory.IsSubnormal
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 75 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Groupstatement and proof · cited by 6,238
- MonoidHomstatement and proof · cited by 3,629
- Subgroupstatement and proof · cited by 3,593
- LE.le.transproof · cited by 3,151
- Subgroup.Normalproof · cited by 334
- Subgroup.mapstatement and proof · cited by 301
- Subgroup.subgroupOfproof · cited by 122
- Subgroup.IsSubnormalstatement and proof · cited by 19
- Subgroup.normal_subgroupOf_iff_le_normalizerproof · cited by 9
- Subgroup.map_monoproof · cited by 8
- Subgroup.map_top_of_surjectiveproof · cited by 7
Cited by2
Results whose statement or proof uses this declaration.
- Subgroup.IsSubnormal.quotientproof · cited by 0
- Subgroup.IsSubnormal.smulproof · cited by 0