Theorems · Theorem · group theory
Subgroup.IsSubnormal.comap
∀ {G : Type u_1} [inst : Group G] {G' : Type u_2} [inst_1 : Group G'] {H' : Subgroup G'} (f : G →* G'),
H'.IsSubnormal → (Subgroup.comap f H').IsSubnormalThe inverse image of a subnormal subgroup under a group homomorphism is a subnormal 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.
- 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.comapstatement and proof · cited by 154
- Subgroup.subgroupOfproof · cited by 122
- Subgroup.IsSubnormalstatement and proof · cited by 19
- Subgroup.comap_monoproof · cited by 11
- Subgroup.comap_topproof · cited by 10
- Subgroup.normal_subgroupOf_iff_le_normalizerproof · cited by 9
- Subgroup.le_normalizer_comapproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- Subgroup.IsSubnormal.subgroupOfproof · cited by 1