Conjugate Element

Given a group with elements A and X, there must be an element B which is a similarity transformation of A,B=X^(-1)AX so A and B are conjugate with respect to X. Conjugate elements have the following properties:

1. Every element is conjugate with itself.

2. If A is conjugate with B with respect to X, then B is conjugate to A with respect to X.

3. If A is conjugate with B and C, then B and C are conjugate with each other.

See also

Conjugacy Class, Conjugate Elements, Conjugate Subgroup, Similar Matrices, Similarity Transformation

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Cite this as:

Weisstein, Eric W. "Conjugate Element." From MathWorld--A Wolfram Web Resource.

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