Theorems · Theorem · group theory
Subgroup.IsSubnormal.of_subsingleton
∀ {G : Type u_1} [inst : Group G] {H : Subgroup G} [Subsingleton ↥H], H.IsSubnormalIf the subgroup H of a group G is trivial, then it is subnormal.
- Defined in
- Mathlib.GroupTheory.IsSubnormal
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 72 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- GroupSubsingleton
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Cites4
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
- Subgroupstatement and proof · cited by 3,593
- Subgroup.IsSubnormalstatement and proof · cited by 19
- Subgroup.eq_bot_of_subsingletonproof · cited by 8
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