Character-conjugate conjugacy classes

This term is related to: linear representation theory
View other terms related to linear representation theory | View facts related to linear representation theory

BEWARE! This term is nonstandard and is being used locally within the wiki. [SHOW MORE]

For its use outside the wiki, please define the term when using it. If you are aware of an equivalent standard term, please leave a comment on the talk page
VIEW: Definitions built on this | Facts about this: (facts closely related to Character-conjugate conjugacy classes, all facts related to Character-conjugate conjugacy classes) |Survey articles about this | Survey articles about definitions built on this
VIEW RELATED: Analogues of this | Variations of this | Opposites of this |
Learn more about terminology local to the wiki | view a complete list of such terminology

Definition

Two conjugacy classes in a group are said to be character-conjugate if for every finite-dimensional indecomposable linear representation (and hence any finite-dimensional linear representation) of the group, the value that the character of the representation takes on both the conjugacy classes is equal.

Relation with other properties

Stronger properties

• Locally conjugate conjugacy classes

Facts

It turns out that for a finite group, and a field whose characteristic does not divide the order of the group, character-conjugate conjugacy classes are the same as locally conjugate conjugacy classes.