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doc(group_theory): fix normalizer docstring (#7231)
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The _smallest_ subgroup of `G` inside which `H` is normal is `H` itself.
The _largest_ subgroup of `G` inside which `H` is normal is the normalizer.

Also confirmed by Wikipedia (see the 5th bullet point under "Groups" at [the list of properties of the centralizer and normalizer](https://en.wikipedia.org/wiki/Centralizer_and_normalizer#Properties)), because it's good to have independent confirmation for something so easy to confuse.
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mguaypaq committed Apr 17, 2021
1 parent 21d74c7 commit 2292463
Showing 1 changed file with 2 additions and 2 deletions.
4 changes: 2 additions & 2 deletions src/group_theory/subgroup.lean
Expand Up @@ -861,8 +861,8 @@ instance center_normal : (center G).normal :=
end

variables {G} (H)
/-- The `normalizer` of `H` is the smallest subgroup of `G` inside which `H` is normal. -/
@[to_additive "The `normalizer` of `H` is the smallest subgroup of `G` inside which `H` is normal."]
/-- The `normalizer` of `H` is the largest subgroup of `G` inside which `H` is normal. -/
@[to_additive "The `normalizer` of `H` is the largest subgroup of `G` inside which `H` is normal."]
def normalizer : subgroup G :=
{ carrier := {g : G | ∀ n, n ∈ H ↔ g * n * g⁻¹ ∈ H},
one_mem' := by simp,
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