Theorems · Theorem · group theory
AddSubgroup.IsSubnormal.comap
∀ {G : Type u_1} [inst : AddGroup G] {G' : Type u_2} [inst_1 : AddGroup G'] {H' : AddSubgroup G'} (f : G →+ G'),
H'.IsSubnormal → (AddSubgroup.comap f H').IsSubnormalThe inverse image of a subnormal additive subgroup under an additive group homomorphism is a subnormal additive subgroup.
- Defined in
- Mathlib.GroupTheory.IsSubnormal
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 73 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- 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.Normalproof · cited by 183
- AddSubgroup.comapstatement and proof · cited by 123
- AddSubgroup.addSubgroupOfproof · cited by 87
- AddSubgroup.IsSubnormalstatement and proof · cited by 17
- AddSubgroup.comap_monoproof · cited by 11
- AddSubgroup.normal_addSubgroupOf_iff_le_normalizerproof · cited by 8
- AddSubgroup.comap_topproof · cited by 7
- AddSubgroup.le_normalizer_comapproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- AddSubgroup.IsSubnormal.addSubgroupOfproof · cited by 1