commSemigroup — Mathlib

English

There is a canonical CoeOut from Sylow p G to Subgroup G, i.e., Sylow p G naturally coextends to a subgroup of G.

Русский

Существуют каноническое вложение (коэрсоу) из Sylow p G в Subgroup G, то есть естественное вложение подгруппы.

LaTeX

$$$\\text{CoeOut}\\ (Sylow\\ p\\ G)\\ (Subgroup\\ G)$$$

Lean4

/-- The center of a magma is commutative and associative. -/
@[to_additive /-- The center of an additive magma is commutative and associative. -/
    ]
instance commSemigroup : CommSemigroup (center M)
    where
  mul_assoc _ b _ := Subtype.ext <| b.2.mid_assoc _ _
  mul_comm a _ := Subtype.ext <| a.2.comm _

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