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

*{{cite book , first = Jean-Pierre , last = Serre , author-link = Jean-Pierre Serre , title = Linear Representations of Finite Groups , url = https://archive.org/details/linearrepresenta1977serr , url-access = registration , series =

Graduate Texts in Mathematics Graduate Texts in Mathematics (GTM) (ISSN 0072-5285) is a series of graduate-level textbooks in mathematics published by Springer-Verlag. The books in this series, like the other Springer-Verlag mathematics series, are yellow books of a standard s ...

, 42 , publisher =

Springer-Verlag Springer Science+Business Media, commonly known as Springer, is a German multinational publishing company of books, e-books and peer-reviewed journals in science, humanities, technical and medical (STM) publishing. Originally founded in 1842 in ...

, location = New York–Heidelberg , date = 1977-09-01 , isbn = 978-0-387-90190-9 , mr = 0450380 , zbl = 0355.20006

Proof

References

Further reading