[Merged by Bors] - feat(group_theory/subgroup/basic): Define characteristic subgroups #9921
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| attribute [class] characteristic | ||
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| @[priority 100] instance normal_of_characteristic [h : H.characteristic] : H.normal := | ||
| ⟨λ a ha b, (set_like.ext_iff.mp (h.fixed (mul_aut.conj b)) a).mpr ha⟩ |
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Can to_additive generate this instance?
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I can't seem to get it to work :(
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| structure characteristic : Prop := | ||
| (fixed : ∀ ϕ : G ≃* G, H.comap ϕ.to_monoid_hom = H) | ||
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| attribute [class] characteristic |
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You can use
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| structure characteristic : Prop := | |
| (fixed : ∀ ϕ : G ≃* G, H.comap ϕ.to_monoid_hom = H) | |
| attribute [class] characteristic | |
| @[class] structure characteristic : Prop := | |
| (fixed : ∀ ϕ : G ≃* G, H.comap ϕ.to_monoid_hom = H) |
to achieve the same goal.
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There is a slight difference. With the current setup, if [h : characteristic H], then you can write h.fixed. With the proposed setup, you have to write characteristic.fixed. This is especially painful if h is not an instance (e.g., in characteristic_iff_comap_eq).
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(I presume this is why subgroup.normal does the same thing)
| ⟨characteristic.fixed, characteristic.mk⟩ | ||
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| @[to_additive] lemma characteristic_iff_comap_le : | ||
| H.characteristic ↔ ∀ ϕ : G ≃* G, H.comap ϕ.to_monoid_hom ≤ H := |
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Please mention this and the next lemmas in the docstring.
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Done (assuming you mean the docstrings for the definitions)
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…9921) This PR defines characteristic subgroups and builds the basic API. Getting `@[to_additive]` to work correctly was a bit tricky, so I mostly just copied the setup for `subgroup.normal`. Co-authored-by: tb65536 <tb65536@users.noreply.github.com>
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…9921) This PR defines characteristic subgroups and builds the basic API. Getting `@[to_additive]` to work correctly was a bit tricky, so I mostly just copied the setup for `subgroup.normal`. Co-authored-by: tb65536 <tb65536@users.noreply.github.com>
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This PR defines characteristic subgroups and builds the basic API.
Getting
@[to_additive]to work correctly was a bit tricky, so I mostly just copied the setup forsubgroup.normal.