center — Mathlib

English

The center of a group G is the set of elements that commute with every element of G.

Русский

Центр группы G — это множество элементов, которые commute со всеми элементами G.

LaTeX

$$$\\uparrow(\\mathrm{center}(G)) = \\mathrm{Set.center}(G)$$$

Lean4

/-- The center of a group `G` is the set of elements that commute with everything in `G` -/
@[to_additive /-- The center of an additive group `G` is the set of elements that commute with
          everything in `G` -/
    ]
def center : Subgroup G :=
  { Submonoid.center G with
    carrier := Set.center G
    inv_mem' := Set.inv_mem_center }

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