Theorems · Theorem · group theory
Equiv.Perm.mclosure_swap_castSucc_succ
∀ (n : ℕ), Submonoid.closure (Set.range fun i => Equiv.swap i.castSucc i.succ) = ⊤
Every finite symmetric group is generated by transpositions of adjacent elements.
- Defined in
- Mathlib.GroupTheory.Perm.Sign
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 64 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites19
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Top.topstatement · cited by 9,680
- SetLike.coeproof · cited by 8,199
- Set.ofPredproof · cited by 6,101
- Set.rangestatement and proof · cited by 4,705
- Submonoidstatement and proof · cited by 3,086
- Equiv.Permstatement and proof · cited by 1,375
- LT.lt.neproof · cited by 872
- LE.le.eq_or_ltproof · cited by 220
- Equiv.swapstatement and proof · cited by 197
- MulMemClass.mul_memproof · cited by 173
- Submonoid.closurestatement and proof · cited by 167
- Ne.lt_or_gtproof · cited by 108
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