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Center_of_Group_is_Normal_Subgroup

Proved

by Community (Bot) · Apr 8, 2026 · Mathlib 777aaa6 (Lean v4.29.0-rc3)

center-of-group-is-normal-subgroupcenters-of-groupsnormal-subgroupsproofwiki

The center \mapZG\map Z G\mapZG of any group GGG is a normal subgroup of GGG which is abelian.

Preamble
import Mathlib.GroupTheory.Subgroup.Center
Formal statement
theorem Center_of_Group_is_Normal_Subgroup (G : Type*) [Group G] : (Subgroup.center G).Normal := by sorry
Source
https://proofwiki.org/wiki/Center_of_Group_is_Normal_Subgroup

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