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[Merged by Bors] - feat(group_theory/subgroup/basic): Cyclic subgroups are commutative #13663

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[Merged by Bors] - feat(group_theory/subgroup/basic): Cyclic subgroups are commutative #13663

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8 changes: 8 additions & 0 deletions src/group_theory/subgroup/basic.lean
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Expand Up @@ -2648,6 +2648,14 @@ begin
exact of_mul_image_zpowers_eq_zmultiples_of_mul,
end

namespace subgroup

@[to_additive] instance zpowers_is_commutative (g : G) : (zpowers g).is_commutative :=
⟨⟨λ ⟨_, _, h₁⟩ ⟨_, _, h₂⟩, by rw [subtype.ext_iff, coe_mul, coe_mul,
subtype.coe_mk, subtype.coe_mk, ←h₁, ←h₂, zpow_mul_comm]⟩⟩

end subgroup

namespace monoid_hom

variables {G' : Type*} [group G']
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