Theorems · Theorem · group theory
IsAddCyclic.exists_generator
∀ {α : Type u_1} [inst : AddGroup α] [IsAddCyclic α], ∃ g, ∀ (x : α), x ∈ AddSubgroup.zmultiples g- Cited by
- 8 results in Mathlib
- Foundations
- Depth 33 from the axioms · uses propext
- Assumes
- AddGroupIsAddCyclic
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.
- AddGroupstatement and proof · cited by 4,410
- AddSubgroupstatement · cited by 3,232
- AddSubgroup.zmultiplesstatement · cited by 493
- IsAddCyclicstatement and proof · cited by 55
- exists_zsmul_surjectiveproof · cited by 2
Cited by8
Results whose statement or proof uses this declaration.
- IsSimpleAddGroup.prime_cardproof · cited by 2
- IsAddCyclic.exists_ofOrder_eq_natCardproof · cited by 1
- AddMonoidHom.isAddCommutative_of_isAddCyclic_of_ker_le_centerproof · cited by 1
- IsAddCyclic.card_nsmul_eq_zero_leproof · cited by 1
- IsAddCyclic.exponent_eq_zero_of_infiniteproof · cited by 0
- IsAddCyclic.extproof · cited by 0
- AddMonoidHom.map_addCyclicproof · cited by 0
- IsAddCyclic.exists_addMonoid_generatorproof · cited by 0