Theorems · Theorem · group theory
Commute.of_orderOf_dvd_two
∀ {G : Type u} [inst : Monoid G] [IsCancelMul G], (∀ (g : G), orderOf g ∣ 2) → ∀ (a b : G), Commute a b- Defined in
- Mathlib.GroupTheory.Exponent
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 34 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- MonoidIsCancelMul
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Monoidstatement and proof · cited by 3,887
- mul_oneproof · cited by 3,885
- mul_assocproof · cited by 1,667
- Commutestatement · cited by 639
- orderOfstatement and proof · cited by 324
- pow_twoproof · cited by 150
- IsCancelMulstatement and proof · cited by 32
- commute_iff_eqproof · cited by 20
- mul_right_injproof · cited by 11
- mul_left_injproof · cited by 8
Cited by1
Results whose statement or proof uses this declaration.
- mul_comm_of_exponent_twoproof · cited by 1