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Theorems · Theorem · group theory

IsCyclic.exists_monoid_generator

∀ {α : Type u_1} [inst : Group α] [Finite α] [IsCyclic α], ∃ x, ∀ (y : α), y ∈ Submonoid.powers x
Defined in
Mathlib.GroupTheory.SpecificGroups.Cyclic.Basic
Cited by
1 results in Mathlib
Foundations
Depth 71 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
GroupFiniteIsCyclic
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

sum_hom_units_eq_zero · cited by 1sum_hom_units_eq_zeroGroup · cited by 6238GroupSubmonoid · cited by 3086SubmonoidFinite · cited by 3029FiniteSubmonoid.powers · cited by 408Submonoid.powersIsCyclic · cited by 122IsCyclicIsCyclic.exists_generator · cited by 14IsCyclic.exists_generatorIsCyclic.exists_monoid_genera…CITED BYCITES

Cites6

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Cited by1

Results whose statement or proof uses this declaration.