isCyclic — Mathlib

English

An instance shows IsCyclic for a simple group.

Русский

Запись допускает цикличность простой группы.

LaTeX

$$IsCyclic α$$

Lean4

@[to_additive]
instance (priority := 100) isCyclic : IsCyclic α := by
  nontriviality α
  obtain ⟨g, hg⟩ := exists_ne (1 : α)
  have : Subgroup.zpowers g = ⊤ := (eq_bot_or_eq_top (Subgroup.zpowers g)).resolve_left (Subgroup.zpowers_ne_bot.2 hg)
  exact ⟨⟨g, (Subgroup.eq_top_iff' _).1 this⟩⟩

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