frattini_characteristic — Mathlib

English

The Frattini subgroup is characteristic in G; it is preserved under all automorphisms of G.

Русский

Фраттини-подгруппа характеристична в G; она сохраняется во всех автоматомах G.

LaTeX

$$$\\operatorname{frattini}(G) \\text{ is a characteristic subgroup of } G$$$

Lean4

/-- The Frattini subgroup is characteristic. -/
instance frattini_characteristic : (frattini G).Characteristic :=
  by
  rw [characteristic_iff_comap_eq]
  intro φ
  apply φ.comapSubgroup.map_radical

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