Theorems · Theorem · group theory
AddSubgroup.isSimpleAddGroup_iff
∀ {G : Type u_1} [inst : AddGroup G] {H : AddSubgroup G},
IsSimpleAddGroup ↥H ↔ H ≠ ⊥ ∧ ∀ H' ≤ H, (H'.addSubgroupOf H).Normal → H' = ⊥ ∨ H' = H- Defined in
- Mathlib.GroupTheory.Subgroup.Simple
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 79 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddGroup
Around this declaration
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Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Top.topproof · cited by 9,680
- Bot.botstatement and proof · cited by 4,720
- AddGroupstatement and proof · cited by 4,410
- AddSubgroupstatement and proof · cited by 3,232
- AddSubgroup.Normalstatement and proof · cited by 183
- AddSubgroup.addSubgroupOfstatement and proof · cited by 87
- IsSimpleAddGroupstatement · cited by 14
- LE.le.ge_iff_eqproof · cited by 12
- AddSubgroup.nontrivial_iff_ne_botproof · cited by 4
- disjoint_of_le_iff_left_eq_botproof · cited by 3
- AddSubgroup.addSubgroupOf_eq_topproof · cited by 3
- AddSubgroup.addSubgroupOf_eq_botproof · cited by 1
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