In mathematics, an induced character is a character

Character (mathematics)

In mathematics, a character is a special kind of function from a group to a field . There are at least two distinct, but overlapping meanings...

 of the induced representation

Induced representation

In mathematics, and in particular group representation theory, the induced representation is one of the major general operations for passing from a representation of a subgroup H to a representation of the group G itself. It was initially defined as a construction by Frobenius, for linear...

 V of a finite group G by W. There is also a notion of induction  of a class function f on H given by the formula


However, if f is a character of the representation W of H, then is a character of the induced representation V.

The basic result is Brauer's theorem on induced characters

Brauer's theorem on induced characters

Brauer's theorem on induced characters, often known as Brauer's induction theorem, and named after Richard Brauer, is a basic result in the branch of mathematics known as character theory, which is, in turn, part of the representation theory of a finite group...

. It states that a character on G is a linear combination with integer coefficients of characters induced from elementary subgroup

Elementary group

In algebra, more specifically group theory, a p-elementary group is a direct product of a finite cyclic group of order relatively prime to p and a p-group. A finite group is an elementary group if it is p-elementary for some prime number p...

s.