Groupprops, The Group Properties Wiki (pre-alpha)

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

This term associates to every group, a corresponding field property. In other words, given a field, every field either has the property with respect to that group or does not have the property with respect to that group

Contents 1 Definition 2 Relation with other properties 2.1 Stronger properties 2.2 Weaker properties 3 Facts

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Definition

A field is said to be character-separating for a group if no two distinct conjugacy classes have the same character value for every representation. In other words, the values of characters of representations separate conjugacy classes.

Relation with other properties

Stronger properties

• Sufficiently large field for a finite group
• Splitting field for a finite group

Weaker properties

• Class-separating field

Facts

Any splitting field for a finite group is character-separating. In particular, any sufficiently large field is character-separating.