English
Let G ≤ H × I be a subgroup with bijective first projection; then G = f.graph for some group hom f : H →* I.
Русский
Пусть G ≤ H × I — подгруппа с биективной первой проекцией; тогда G = f.graph для некоторого гомоморфизма f : H →* I.
LaTeX
$$$\\exists f : H \\to^* I, G = f.graph$$$
Lean4
/-- The `n`th power map on a commutative monoid for a natural `n`, considered as a morphism of
monoids. -/
@[to_additive (attr := simps) /-- Multiplication by a natural `n` on a commutative additive monoid,
considered as a morphism of additive monoids. -/
]
def powMonoidHom (n : ℕ) : α →* α where
toFun := (· ^ n)
map_one' := one_pow _
map_mul' a b := mul_pow a b n
