Theorems · Theorem · group theory
Group.IsPerfect.center_quotient_center_eq_bot
∀ (G : Type u_1) [inst : Group G] [Group.IsPerfect G], Subgroup.center (G ⧸ Subgroup.center G) = ⊥
Grün's lemma
- Defined in
- Mathlib.GroupTheory.IsPerfect
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 94 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- GroupGroup.IsPerfect
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
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 and proof · cited by 4,720
- Subgroupstatement and proof · cited by 3,593
- HasQuotient.Quotientstatement and proof · cited by 2,301
- Subgroup.comapproof · cited by 154
- Subgroup.centerstatement and proof · cited by 121
- QuotientGroup.mk'proof · cited by 90
- Subgroup.upperCentralSeriesproof · cited by 51
- QuotientGroup.ker_mk'proof · cited by 18
- Group.IsPerfectstatement and proof · cited by 17
- QuotientGroup.mk'_surjectiveproof · cited by 15
- Subgroup.upperCentralSeries_oneproof · cited by 7
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