eq_iff_eq_on_generator — Mathlib

English

Two groups of prime order p are isomorphic.

Русский

Две группы порядка простого p изоморфны.

LaTeX

$$G \cong^* G' \text{ when } |G|=|G'|=p \text{ prime}$$

Lean4

/-- Two group isomorphisms `G ≃* G'` are equal if and only if they agree on a generator of `G`. -/
@[to_additive /-- Two isomorphisms `G ≃+ G'` of additive groups are equal if and only if they agree
    on a generator of `G`. -/
    ]
theorem eq_iff_eq_on_generator (f₁ f₂ : G ≃* G') : f₁ = f₂ ↔ f₁ g = f₂ g :=
  (Function.Injective.eq_iff toMonoidHom_injective).symm.trans <| MonoidHom.eq_iff_eq_on_generator hg ..

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