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Theorems · Theorem · group theory

isSimpleAddGroup_iff

∀ (A : Type u_2) [inst : AddGroup A],
  IsSimpleAddGroup A ↔ Nontrivial A ∧ ∀ (H : AddSubgroup A), H.Normal → H = ⊥ ∨ H = ⊤
Defined in
Mathlib.GroupTheory.Subgroup.Simple
Cited by
1 results in Mathlib
Foundations
Depth 17 from the axioms · uses propext, Quot.sound
Assumes
AddGroup
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

AddSubgroup.isSimpleAddGroup_iff · cited by 0AddSubgroup.isSimpleAddGr…Top.top · cited by 9680Top.topBot.bot · cited by 4720Bot.botAddGroup · cited by 4410AddGroupAddSubgroup · cited by 3232AddSubgroupNontrivial · cited by 2416NontrivialAddSubgroup.Normal · cited by 183AddSubgroup.NormalIsSimpleAddGroup · cited by 14IsSimpleAddGroupIsSimpleAddGroup.casesOn · cited by 1IsSimpleAddGroup.casesOnisSimpleAddGroup_iffCITED BYCITES

Cites8

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Cited by1

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