Artin's theorem on induced characters
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
gollark: You can't have internet connectivity on Mars without GTech™ anomalous bee spheres™. Light-lag's too high.
gollark: Correction: 9 out of 9 dentists.
gollark: Since the internet involves money, according to 9 out of 10 surveyed dentists at GTech™.
gollark: I mean, regardless on your opinions of it as a substitute for in-person communication, you're still participating in the economy™.
gollark: "Internet" and "on your own" don't particularly fit together though?
References
- Serre, Jean-Pierre (1977-09-01). Linear Representations of Finite Groups. Graduate Texts in Mathematics, 42. New York–Heidelberg: Springer-Verlag. ISBN 978-0-387-90190-9. MR 0450380. Zbl 0355.20006.CS1 maint: ref=harv (link)
This article is issued from Wikipedia. The text is licensed under Creative Commons - Attribution - Sharealike. Additional terms may apply for the media files.