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[Merged by Bors] - doc(group_theory/sylow): Expand Frattini's argument docstring #10174

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[Merged by Bors] - doc(group_theory/sylow): Expand Frattini's argument docstring #10174

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3 changes: 2 additions & 1 deletion src/group_theory/sylow.lean
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Expand Up @@ -217,7 +217,8 @@ lemma card_sylow_dvd_index [fact p.prime] [fintype (sylow p G)] (P : sylow p G)
card (sylow p G) ∣ P.1.index :=
((congr_arg _ (card_sylow_eq_index_normalizer P)).mp dvd_rfl).trans (index_dvd_of_le le_normalizer)

/-- Frattini's Argument -/
/-- Frattini's Argument: If `N` is a normal subgroup of `G`, and if `P` is a Sylow `p`-subgroup
of `N`, then `N_G(P) ⊔ N = G`. -/
lemma sylow.normalizer_sup_eq_top {p : ℕ} [fact p.prime] {N : subgroup G} [N.normal]
[fintype (sylow p N)] (P : sylow p N) : ((↑P : subgroup N).map N.subtype).normalizer ⊔ N = ⊤ :=
begin
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