Theorems · Theorem · group theory
Subgroup.IsSubnormal.exists_chain
∀ {G : Type u_1} [inst : Group G] {H : Subgroup G},
H.IsSubnormal → ∃ n f, Monotone f ∧ (∀ (i : ℕ), ((f i).subgroupOf (f (i + 1))).Normal) ∧ f 0 = H ∧ f n = ⊤Alias of the forward direction of Subgroup.IsSubnormal.isSubnormal_iff.
A characterisation of satisfying IsSubnormal in terms of chains of subgroups, each normal in
the following one.
The sequence stabilises once it reaches ⊤, which is guaranteed at the asserted n.
- Defined in
- Mathlib.GroupTheory.IsSubnormal
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 71 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Group
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Top.topstatement · cited by 9,680
- Groupstatement and proof · cited by 6,238
- Subgroupstatement and proof · cited by 3,593
- Monotonestatement · cited by 1,397
- Subgroup.Normalstatement · cited by 334
- Subgroup.subgroupOfstatement · cited by 122
- Subgroup.IsSubnormalstatement · cited by 19
- Subgroup.IsSubnormal.isSubnormal_iffproof · cited by 1
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.