# Artin's theorem on induced characters

From HandWiki

In representation theory, a branch of mathematics, **Artin's theorem**, introduced by E. Artin, states that a character on a finite group is a rational linear combination of characters induced from cyclic subgroups of the group.
There is a similar but somehow more precise theorem due to Brauer, which says that the theorem remains true if "rational" and "cyclic subgroup" are replaced with "integer" and "elementary subgroup".

## Proof

## References

- Serre, Jean-Pierre (1977-09-01).
*Linear Representations of Finite Groups*. Graduate Texts in Mathematics,**42**. New Yorkâ€“Heidelberg: Springer-Verlag. ISBN 978-0-387-90190-9. https://archive.org/details/linearrepresenta1977serr.

## Further reading

Original source: https://en.wikipedia.org/wiki/Artin's theorem on induced characters.
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