Theorems · Theorem · group theory
IsSimpleGroup.comm_iff_isSolvable
∀ {G : Type u_1} [inst : Group G] [IsSimpleGroup G], (∀ (a b : G), a * b = b * a) ↔ Group.IsSolvable G- Defined in
- Mathlib.GroupTheory.Solvable
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 76 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- GroupIsSimpleGroup
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Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
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- mul_inv_eq_oneproof · cited by 20
- Subgroup.mem_botproof · cited by 11
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