Theorems · Theorem · group theory
Subgroup.eq_bot_of_subsingleton
∀ {G : Type u_1} [inst : Group G] (H : Subgroup G) [Subsingleton ↥H], H = ⊥- Defined in
- Mathlib.Algebra.Group.Subgroup.Lattice
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 20 from the axioms · uses propext, Quot.sound
- Assumes
- GroupSubsingleton
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- Bot.botstatement · cited by 4,720
- Subgroupstatement and proof · cited by 3,593
- Subgroup.eq_bot_iff_forallproof · cited by 7
- Subgroup.coe_oneproof · cited by 6
- Subgroup.coe_mkproof · cited by 5
Cited by8
Results whose statement or proof uses this declaration.
- IsQuotientCoveringMap.monodromyPerm_injectiveproof · cited by 2
- Subgroup.exists_right_complement'_of_coprimeproof · cited by 2
- Subgroup.coe_eq_singletonproof · cited by 2
- Subgroup.eq_bot_of_card_eqproof · cited by 2
- Subgroup.eq_bot_of_card_leproof · cited by 1
- Subgroup.IsSubnormal.of_subsingletonproof · cited by 0
- SpecialLinearGroup.center_eq_bot_of_finrank_le_oneproof · cited by 0
- Sylow.eq_bot_of_oneproof · cited by 0