Theorems · Theorem · group theory
isOfFinOrder_of_finite
∀ {G : Type u_1} [inst : LeftCancelMonoid G] [Finite G] (x : G), IsOfFinOrder x- Defined in
- Mathlib.GroupTheory.OrderOfElement
- Cited by
- 14 results in Mathlib
- Foundations
- Depth 68 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- LeftCancelMonoidFinite
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Set.ofPredproof · cited by 6,101
- Finitestatement and proof · cited by 3,029
- Set.toFiniteproof · cited by 174
- IsOfFinOrderstatement and proof · cited by 113
- LeftCancelMonoidstatement and proof · cited by 28
- infinite_not_isOfFinOrderproof · cited by 1
Cited by15
Results whose statement or proof uses this declaration.
- orderOf_posproof · cited by 15
- mem_powers_iff_mem_zpowersproof · cited by 6
- Fintype.card_zpowersproof · cited by 5
- orderOf_powproof · cited by 5
- AddChar.norm_applyproof · cited by 2
- isOfFinOrder_iff_isUnitproof · cited by 1
- powersEquivPowersproof · cited by 1
- mem_zpowers_iff_mem_range_orderOfproof · cited by 1
- LinearEquiv.isOfFinOrder_of_finite_of_span_eq_top_of_mapsToproof · cited by 1
- exists_root_adjoin_eq_top_of_isCyclicproof · cited by 1
- Polynomial.irreducible_of_dvd_cyclotomic_of_natDegreeproof · cited by 1
- exists_zpow_eq_oneproof · cited by 0