Theorems · Theorem · group theory
Group.isSolvable_of_comm
∀ {G : Type u_3} [hG : Group G], (∀ (a b : G), a * b = b * a) → Group.IsSolvable G- Defined in
- Mathlib.GroupTheory.Solvable
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 72 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Group
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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
- CommGroupproof · cited by 990
- DivInvMonoidproof · cited by 103
- Group.IsSolvablestatement · cited by 46
- Group.casesOnproof · cited by 2
Cited by4
Results whose statement or proof uses this declaration.
- gal_X_pow_sub_C_isSolvable_auxproof · cited by 1
- gal_X_pow_sub_one_isSolvableproof · cited by 1
- IsSimpleGroup.comm_iff_isSolvableproof · cited by 0
- isSolvable_of_commproof · cited by 0