Centralizer (original) (raw)

TOPICS

Algebra Applied Mathematics Calculus and Analysis Discrete Mathematics Foundations of Mathematics Geometry History and Terminology Number Theory Probability and Statistics Recreational Mathematics Topology

Alphabetical Index New in MathWorld

• Algebra
• Group Theory
• Group Properties

The centralizer of an element of a group is the set of elements of which commute with ,

Likewise, the centralizer of a subgroup of a group is the set of elements of which commute with every element of ,

The centralizer always contains the group center of the group and is contained in the corresponding normalizer. In an Abelian group, the centralizer is the whole group.

See also

Abelian Group, Group, Group Center, Normalizer,Subgroup

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Cite this as:

Weisstein, Eric W. "Centralizer." FromMathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Centralizer.html

Subject classifications

• Algebra
• Group Theory
• Group Properties