commGroup — Mathlib

English

The alternating group is a characteristic subgroup of the permutation group.

Русский

Чередующаяся группа является характеристической подгруппой группы перестановок.

LaTeX

$$$$\\operatorname{IsCharacteristic}(\\operatorname{alternatingGroup}(\\alpha), \\operatorname{Perm}(\\alpha)).$$$$

Lean4

/-- A cyclic group is always commutative. This is not an `instance` because often we have a better
proof of `CommGroup`. -/
@[to_additive /-- A cyclic group is always commutative. This is not an `instance` because often we have
          a better proof of `AddCommGroup`. -/
    ]
def commGroup [hg : Group α] [IsCyclic α] : CommGroup α :=
  { hg with mul_comm := commutative.comm }

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