DefinitionDefinition: Literature-sourcedProof: Not applicableaudited 2026-08-11

How statement and proof provenance work

The first chip identifies the source of the statement or construction; the second identifies the source of its local proof or verification.

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These labels describe origin, not correctness: citations and verification chips remain separate evidence.

The conjugacy class ${Cl}_{G} (x)$ and centralizer $C_{G} (x)$ of an element

Definition

Let $G$ be a group and $x \in G$ (Group and abelian group). The conjugacy class of $x$ is

${Cl}_{G} (x) : = {g x g^{- 1} : g \in G} .$

The centralizer of $x$ is

$C_{G} (x) : = {g \in G : g x = x g} = {g \in G : g x g^{- 1} = x} .$

The subgroup property implicit in the notation is proved in $C_{G} (x)$ and $N_{G} (H)$ are subgroups of $G$ ↗.

Depends on

Group and abelian group

Dependency tree · 2 levels

Sources

T. W. Judson, Abstract Algebra: Theory and Applications, 14.2