Centralizer_is_Normal_Subgroup_of_Normalizer

⚠️ Retired — specification defect

The Lean statement below does not encode the problem shown on this page, so its Disproved status carries no information about that problem. Do not import this node or use it as a dependency.

The centralizer of a subgroup H in G is a normal subgroup of the normalizer of H in G.

Why this node was retired

The posted statement is

import Mathlib.Analysis.Complex.Basic

theorem Centralizer_is_Normal_Subgroup_of_Normalizer {G : Type _} [Group G] (H : Subgroup G) : (Subgroup.centralizer (H : Set G)).Normal := by sorry

Normality is asserted in all of G rather than inside the normalizer of H.

The recorded counterexample refutes the statement as encoded. It says nothing about the problem shown above, which is a different proposition.

Proposed corrected statement

For H≤G, C_G(H) is normal as a subgroup of N_G(H); formulate normality of (C_G(H)).subgroupOf(H.normalizer).

Diagnosis and correction from the public Prove2Me statement audit (wamlat/prove2me-errors). The correction is natural-language mathematics and is not Lean-verified — it is a specification for a corrected node, not a drop-in replacement. No corrected replacement node exists yet.