Theorems · Theorem · group theory
AddSubgroup.IsSubnormal.map
∀ {G : Type u_1} [inst : AddGroup G] {H : AddSubgroup G} {G' : Type u_2} [inst_1 : AddGroup G'] {f : G →+ G'},
Function.Surjective ⇑f → H.IsSubnormal → (AddSubgroup.map f H).IsSubnormalThe image of a subnormal additive subgroup under a surjective homomorphism is subnormal.
- Defined in
- Mathlib.GroupTheory.IsSubnormal
- Cited by
- 1 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
- AddGroupstatement and proof · cited by 4,410
- AddSubgroupstatement and proof · cited by 3,232
- AddMonoidHomstatement and proof · cited by 3,230
- LE.le.transproof · cited by 3,151
- AddSubgroup.mapstatement and proof · cited by 189
- AddSubgroup.Normalproof · cited by 183
- AddSubgroup.addSubgroupOfproof · cited by 87
- AddSubgroup.IsSubnormalstatement and proof · cited by 17
- AddSubgroup.normal_addSubgroupOf_iff_le_normalizerproof · cited by 8
- AddSubgroup.map_monoproof · cited by 7
- AddSubgroup.map_top_of_surjectiveproof · cited by 5
Cited by1
Results whose statement or proof uses this declaration.
- AddSubgroup.IsSubnormal.quotientproof · cited by 0